I don't care for the framing as player entitlement, but I do agree with the premise for a specific framing of "gaming." Rule of Cool is usually a player forward means of shifting the structure of the game into negotiation. Players set out what they'd like to happen, GMs set costs or risks, and the currency added to either side is the perceived "coolness" favor by both parties.
I don't really like negotiation gameplay in general, and I think it's even worse when you're playing with a currency that has variable value to all the players involved in some incalculable, unknowable way. If there existed some other gameplay loop, where the players are presented challenges and leverage abilities, resources and some time/action economy to overcome them, RoC can break that, turning the same into a different, and in my opinion, worse game.
However, there exist modes of play that are entirely negotiation based to begin with, and RoC in those contexts is mostly just suggesting value should be assigned to the "coolness" factor when using them. If that's already the game being played, I have significantly less qualms, though I do like and way of formalizing its value, maybe using a boon/bane system, or meta currency.