I'm old enough to remember thinking Palpatine looked like that because he was really, really old, which I assume was the original intension (somewhat carried over in AOTC where Palpatine is already getting pale and wrinkly but ignored in ROTS where he seems to have rejuvenated).

I started to think they were going to pull some twist where Palpatine and Sidious were seperate characters which would somehow merge.

My favorite theory was that the ambitious and greedy Palpatine was slowly absorbing the dark sorceror Sidious and stealing his power which is why they looked and sounded the same.