II don't hear of any NFL fans pretending to be a celebrity football hero; instead they're content to go to games, buy officially sponsored apparel and support their favorite team.
Wassup?!
I'm guessing that it has to do with the probability of success.
I'm not a sports fan, but I know many of them, and they can name the members of teams and what their records are, and all that info is readily available to the average person from multiple sources, so a person claiming to have been on a team would probably be outed immediately. The same would be true if someone claimed to have been a rock star or a top Hollywood actor, or if someone claimed to be the President. A celebrity would probably also have lots of money and a fancy car, making the financial requirements difficult for the fake.
Military background is far more difficult for the average person to check.
There have been people with fake claims to European royalty, somehting difficult for most to check, and lots of people with fake degrees. Some popular "doctors" have mail order degrees.