1. PEOPLE WHO SAY THEY HAVE A FAMOUS PAST LIFE DO IT FOR ATTENTION 
Naturally, folks will chalk up another's famous past life story as an attempt to be noticed. It makes perfect sense as in all areas of life, from the workplace or to hanging out at your favorite coffeehouse/watering hole, you'll find these types of individuals. Even within the family dynamic, there are always those few people who thrive on attention and love all eyes to be on them. Online? It's worse!
Reincarnation circles are no different with their mix of personalities and roles. It's not that strange for someone to come out with an FPL first thing in order to shock or to be admired. Even though the more seasoned reincarnationists out there usually can see through this and not take the bait, there are some who gush over the princess/politician/guitar hero. Thus, the attention seeker gets what they want, and it goes on and on and on until the person loses interest and goes elsewhere.
But a lot of times, an individual will 'come out' with a Famous Past Life after much thought and with their story worded carefully. They know you may think they're nuts. They know once they put it out there, there is no going back. They know they may be asked for their research. They know they may be ridiculed and all about the FPL stigma. Regardless, they're want to talk about it and for this sort of person, it's not for something shallow like...attention. There's something deeper behind it, and guess what? They know this, too.

IT IS TRUE that when those with legit FPLs come out with their story, they may garner some extra interest. It is also true that a legit FPL subject can get put on the 'looking for attention' heap because, as someone with a famous past and carrying possible charisma, they could just naturally be the type of person to attract others. 

2. MEMORIES & VERIFICATIONS COME TO YOU EASILY
I asked my son, who is just a regular dude, what his first assumption would be if someone said they were famous in a past life. He thought about it and replied, 'Probably that it would be easier to have memories.' I think he has a point. I also think it is assumed that an FPL is easier to get verifications for. It's not surprising some believe this, as a ton of info is just a Google search away and, even before the internet, books and documentaries could be accessed.
But *is* it true? From my personal experience, not really. Memories themselves, which came frequently when I was younger, dwindled out as I aged, which is a fairly common thing. Neither did I notice that I had more memories than other people who had been working with reincarnation the same amount of time that I had. As for verifications, most of them did not come from some online search. They took a lot of digging, reading, and the questioning of experts. I still have stuff shelved, unverified and waiting. Most of the information that was readily available, the surface stuff, I didn't actually remember and therefore it was of no help.

IT IS TRUE that memories of famous people can sometimes come more often due to more frequent triggering. I also will agree that if you do have a memory and don't have any luck finding the actual event, there is still enough information out there to give you the OK if what you remember is plausible or not. 

3. YOU WILL LOOK THE SAME NOW AS YOU DID IN THE PAST 
How many people have found themselves on Walter Semkiw's site, turning your phone or cocking your head to the side to see the photographic 'evidence' of the famous past life cases he's scrounged up over the years, trying to make connections between eyes, noses, and brows? How many times has that meme of Nic Cage's supposed reincarnations turned up on Facebook or, worse, on reincarnation discussion boards themselves? People can resemble each other, past life or no past life. On my way to work last Thursday, I could of sworn I saw both Eva Braun and Bernie Sanders on my bus. Who'da thunk it? I should of asked for autographs.
No. I don't think people always have to resemble themselves. I think it's more interesting how a person carries themselves or hold the same mannerisms from life to life. Appearance alone? Not so convincing.

IT IS TRUE that some people have a marked resemblance. I have been blown away by some of the cases on the MPL forum, even when race or gender were completely different. I am not sure if it is just coincidence or I am seeing only what I want to see, though. 
There could be some sort of method that causes physical traits to carry over, which may also explain why some people have pl-related birthmarks or certain ailments. 

4. YOU REMEMBER A LOT OF FAMOUS EVENTS
Fantasy: You're so excited...you found a plausible Marilyn Monroe! Ten points for you, eh? But when you ask her how it was to film the skirt scene or the Diamonds Are A Girl's Best Friend number, she says she doesn't remember that. Hey, is this Marilyn Monroe or not? Maybe she's one of those attention-seekers listed above...
Reality: If someone with an FPL remembers a lot of famous events, and not much else, it's possible they're not being entirely honest due to either not being the real person or fluffing up their legit experience because they think it's expected. (<----don't do this) Hey, there's a lot more to a life than just the famous bit the public sees, and it could be that those are the things remembered, not the 15-seconds of film the entire world has memorized. 

IT IS TRUE that famous events can be remembered...and in better detail than what the books and documentaries can tell you. But don't think that these 
famous memories are in any way better than 'regular' ones. They may be more interesting to others, but to the person remembering, a quiet memory with a loved one could possibly be the most cherished by far. 

5. IT'S SO COOL TO HAVE A FAMOUS PAST LIFE!
When we think of fame, we think of famous people and all the things they have: they are popular, they probably have money, they seem very confident and they appear to excel in everything that they do. Maybe beautiful, probably intelligent, complete trendsetters...Even those with more negative past lives have admirers of their misunderstood, dark glamour. What's not to like?
But when you actually experience a Famous Past Life, it doesn't feel that way. For one, you can't say anything due to not being believed...or worse, BEING believed and then hounded. People will doubt your sanity. Others will tell you to stop living in the past more often than if you had a non-FPL. Books, movies, and other related material will never get it right. Twenty other people say they're you. There is a tremendous sense of loss and other feelings you can't properly discharge because the big F-word keeps you tied down. There is this image. People's expectations of you are different. Some get tired of hearing your griping because hey, you were famous...what do you have to complain about?? Having no real outlet can be frustrating. Even when you are over it, something always comes along (a movie, an anniversary) that pulls you right into it again.

IT IS TRUE that lot of the things mentioned above happen to all reincarnations, not just the famous ones. But it seems like there is a lot less judgement for those lives as opposed to the famous, making the burden all the heavier.

And lastly, the one stereotype that seems to override all...

6. EVERYONE THINKS THEY'RE SOMEONE FAMOUS
I believe this reaction is the most common assumption out there. Even people who don't discuss reincarnation or know about past lives at all will quip, "Oh yeah, everyone thinks they're Napoleon or Cleopatra!" if the subject is brought up. 
Actually, no. Everyone thinks they're Reinhard Heydrich or Tatiana Romanov, but I digress...

I do not believe that, out of all the people in this world who believe in reincarnation, a staggering number believe they were someone famous. Even if you look at Western culture, most stories out there are same-family reincarnation or just spooky things a kid has said. A Google search will show most stories consist of fairly ordinary people living fairly ordinary lives. Within my own family, the same people whom I felt I could never fit in with due to pl reasons, we had brief brushes with reincarnation: one of my mom's sisters, who is big into church and Jesus, always thought she had a life in the '20s and would talk about it sometimes. My son, who lives with reincarnation talk around him and couldn't be less interested, could tell me his past life name at age 3 or 4. Even an interview with a screenwriter I read a few days ago revealed that the man was influenced by stories of children's past lives and had talked about his previous death as a small child (his parents told him when he was an adult). 

IT IS TRUE that when people gather online to talk about reincarnation, there are a fair amount of FPLs represented. One large forum in particular will have folks saying they have hardly any members with FPLs, but when I have actually looked at users most active there, almost all of them have had at least one notable life. Here on MPL, you could say the same.
Excluding the possibility that FPL stories simply stand out more against others, giving the impression that there are more of those Heydrichs and Tatianas running around than there really are, it could be that FPLers went online to discuss reincarnation where there is a veil of anonymity. Someone who is the reincarnation of their own uncle may be just fine discussing their challenges at home (or on Facebook, to bring in another current thread), but someone with an FPL perhaps wouldn't go about it the same way. 
It also can be that it seems like so many folks online have FPLs because they're new to the subject and are wrong. Frequently, people will latch their memories onto a famous person because it's the easiest, more obvious target.

My take is that, though it's understandable that FPLs come under serious scrutiny, famous people do reincarnate. Though I am the first to cock an eyebrow and not take a lot of cases seriously, I do understand the struggles and misconceptions. I think it would be so beneficial if FPLs, with more solid evidence than 'we share the same birthday', were more accepted. When historical research gets put on its head due to the real person giving testimony or baddie historical figures are reborn to be just fine, that would sure put a different spin on how others see the world, wouldn't it?