Your points about pool of addressable players and temperament are both fair, the latter being what I was trying to say about a keeper being less of a team player because by definition their role is an essentially isolated one. Whether they're headcases because of that, or whether they gravitate to the role because they're headcases, is a debate for the ages.
I'm not entirely convinced about the name recognition thing though. Of course that makes a difference with the biggest names in the game, but there aren't that many of them. There's at least one former keeper on every pro club's coaching team what with needing a goalkeeping coach and all, you'd think that at least a few would work their way up to bigger jobs if they were suited to doing them.