The problem is worse than that:
1. The largest NES cartridge is 64MB, a PS1 CD is 10x that, so imagine 30 carts
2. A lot of the data across the 3 discs is actually the same data. Think character models and attack animations for your party members, locations you can revisit at any time, the base world map, common soundtracks, etc. The disk to disk differences were mostly things like FMVs and event soundtracks as a result. So the minimum data for the game to run would exceed 1 cartridge. So not only would you have to swap discs at certain points in the story, you'd have to swap them at other points, e.g. because you were backtracking. Trying to gather a spell from a starter dungeon for Beta? Please remove Vincent from your party and insert cartridge 2.
> The largest N64 cartridge is 64MB
Hopefully it was clear I meant N64, not NES from context and the PS1 comparison