You’re right, this sounds extremely entitled. The mere fact that you’re considering sitting out of college for an entire year is the definition of being unhappy with the colleges that have admitted you, and of being insulted, not humbled, at their decisions.
Aside from that observation, I won’t advise you whether you should take a gap year or enroll in a non-Princeton university with the plans to transfer as soon as you can. That is a decision that should involve your parents. If they support either of those decisions, that is all that matters. Personally, if my child was in this situation, I would not consider either option a reasonable or mature decision. But again, your parents know your situation better - maybe they will recognize a factor that makes your wish to sit out reasonable.