I honestly think we're all overestimating the chance of scum fakeclaiming here tbh. Like can anyone tell me what would be the benefit of doing so as compared to scum just claiming their real game?
I was thinking about this last game when Earth decided to fake claim his game. I'd say there are two benefits.
First, if the game you currently have limits your options or overlaps a lot with other games, faking a claim nets you opportunities to select from a different set. It requires analysis of the game you're choosing and some analysis of the others in play, but depending on those factors, there may be a valid reason to switch.
Second, though this came up much later in the last game, is the possibility that town could use it to focus their PoE a bit by considering the ways scum in a given game could have manipulated their results. Casey correctly called out that I was probably the Ninja in the last game because he noted that there was a Ninja in my game and he hadn't seen me move when I attempted to perform the NK. It's not proof positive, but it does allow for more than just guessing about probable scum roles if scum claims their own game. If they claim a different game, that may be a means to misdirect lynches instead.