Is there an in game need for the 60 cards like the Were Rabbit Finale isn't accessible without them or is there some other reason that isn't really stated?

Update, In order to reach the fair at this moment in time you need 60 cards

Yeah that's literally the only reason for the 60 card limit, if there was some way to get to the Fairground without that it would make the game 1000x shorter probably

Would it be faster to get certain other cards?

The route I followed was pretty much doing all the cards the game forces you to do anyway, then get any ones lying around that aren't too far out of the way