my 2 cents: it is obvious to want to know the outcome of the game, moreover when one invested significant effort in terms of money and time. We name it curiosity, which is good habit for a good manager/business person.
Everyone is concerned about him/herself at first and we name it egoism. Is it OK? I think yes, if it does not substantially hurt someone else's interests. Even if it does, an egoist should be concerned about the ourcome of his/her decisions. What's a donwside/hurt of playing a game named "admissions process"? It is a rejection. All of those accepting the game adhere to strict rules and regulations, want to win and realize that they can loose it, if the counterpart (other more quailified candidates) is stronger. Is the project subjective? Yes, therefore everyone is applying to other schools to secure at least one winning outcome.
Even if one was accepted to multiple schools, he/she will choose only one school, allowing others waitlisted candidates to get in.