To render a single frame of a scene in a video game, a load of calculations have to be done. The nicer the graphics, and the higher the resolution, the more calculations have to be done to render the frame.

At 120Hz the console can dedicate half the computation time per frame than at 60Hz and a quarter of the time that it can dedicate at 30Hz.

So for developers to make games with the best possible graphics, they dial down the frame rate to allow for more computational time per frame.

It's also not just graphics, imagine a game with a lot of characters on screen. The game has to compute what each of those characters are doing, their movement e.t.c every frame. The game might support 50 characters on screen at 120Hz and 100 at 60Hz. The 100 character game may be better gameplay wise, so that's what's chosen.

Unless you're playing competitively, or on the absolute hardest difficulties, then honestly above 60Hz doesn't affect your experience that much (especially with a controller).

Its basically zero developer effort to add in an option to reduce graphics for higher FPS - and that only needs to sell you a handful more copies of the game to have been worth doing.