The reason that you need the different memory cards is plain and simple, and can be summed up in one word, ARCHITECTURE. The architecture of a PS1 game looks for the corresponding hardware for a memory card to save to.
There is no EASY way around this problem (yes, I said easy, because it may be able to be circumvented, but would likely drain the system resources to do so). To do so, there would have to be some type of emulation within a ROM on the motherboard for when a load/save function is called from a PS1 game, and emulation takes away cycles, and you should see where this is going.
Another point is that the method of PS1 saves only to a PS1 memory card preserves the portability of the game save. A save on a PS1 card can be used not only on all PS2 units, but all PS1 units as well. A save on a PS2 card would restrict the read to only PS2 machines.
Hopefully this clears things up for you guys (and gals).