I thought there were many aspects of the games directly tied to fram rate.
I know that, at least in the case of mario 64, Speed runners abuse game mechanics tied to frame rate to perform tricks such as backwards long jump and other door hacks. Marios eyes blinking are tied to frame rate, they used this to identify faked speed runs in some cases.
Yes. I know Zelda Ocarina of Time has many things, including walking speed, tied to framerate because of ZFG. Also, the 3DS remake reused a lot of the code and several things tied to framerate got quicker because it ran at 30 fps instead of 20. Items despawn quicker because they despawn at a set amount of frames.