No, that's just me not thinking carefully. Of course the players can pool tickets. Although with the arcade games, one of them setting a high score makes it harder for the others to beat it. It does create a separate issue for small groups as you say.
There is also the trap of buying a souvenir and only being told afterwards that you needed those tickets to leave, which could set even a larger group short. Overall, the idea of being trapped in a supposedly relaxing location until you have exhaustively done all the things and pretended to have a good time is thematically strong but maybe a bad gameplay experience, so I'd build in more shortcuts for a bored party (unless the desired outcome is that they murder the mascot or raid the ticket-printing facilities).