Well, I almost only play Playstation and Nintendo first party games. They are always the decider for me if I buy a system or not. This generation I did not buy a PS4 since it only got 4 games that I'm interested in, all of them first party titles. I will play them on the PS5 instead.
I think first party titles are important in the sense that they are built with a specific system in mind. Taking advantage of that systems capabilities while ignoring any requirements on other systems that could hold the game back.