The way ‘loading’ used to work in the old days is that everything needed for one level or area of a game was fetched into memory from the slow HDD and once it was loaded, it’s all ready to play and you don’t need the HDD anymore.

Games now have a lot of high-resolution textures and assets that are constrained by ram size and by video memory size, such that loading a whole level upfront isn’t going to work. Instead the game will be loading in assets from disk as you play, swapping things in and out. And so for that to work effectively, faster storage is required because you are using the storage throughout gameplay, not only at the beginning.