I am hoping for a similar result (also didn't finish Prince of Persia at the time). I mean - in the meantime, I got pretty far in Super Meat Boy. Prince of Persia looks like a walk in the park in comparison.
Maybe such controls were necessary for animation reasons. You can't jump while both feet are in the air from running, and you can't make doing that look realistic.
I think, beating Aladdin (1993) on PC did help a lot: it was a more challenging game that required getting used to precise controlling the character. Prince of Persia has rather slow animations, and thus you don't even need a quick reflexes to beat it, just learn the levels and know where you need to move in a certain way.