Oscar-winner Edmond O'Brien was one of the most-respected character actors in American cinema, from his heyday of the mid-1940s through the late 1960s.
An interesting quote is attributed to him which seems to have two versions although it may be two quotes expressed differently at different times.
IMDb - Versatility is a dangerous thing. It's very satisfying to portray many types of roles, but often your own identity gets lost. Seldom does a producer say, "This is an Eddie O'Brien part." On the other hand, while the rewards may be great in fame and financially for stars, the work becomes monotonous. No actor who plays himself is a happy person.
Wikipedia - "The funny thing about Hollywood is that they are interested in having you do one thing and do it well and do it ever after," said O'Brien. "That's the sad thing about being a leading man – while the rewards may be great in fame and finances, it becomes monotonous for an actor. I think that's why some of the people who are continually playing themselves are not happy.
O'Brien appears to be saying that the world of a cinema star can be an unhappy one because playing yourself over and over again is monotonous. Yet it is also possible that stars playing themselves get to know themselves and their personal limitations too well. Maybe that is a source of unhappiness too.
In a similar vein this may be why politicians put on an act. A political public persona may be odious but if it isn't thought to be real no damage is done to the self-esteem behind the act.
Or they are mostly thick-skinned swine through and through.