Why was this game coded for 32-bit systems?

I guess this is a little rant, question, and "what if" discussion of the decisions the devs made back in the 2000s.

I have very little experience in coding (so please, anyone who knows better, correct me!) but from my understanding, some of the modern day performance limits of the game come from the fact that it can't utilize all of the ram due to it being a 32-bit program.

Why did the devs decide to build such an ambitious game on 32-bit when 64-bit had been available for a few years at that point? It wasn't like many 32-bit computers in 2009 could have run TS3 anyways (or computers in general). The whole open world concept seems pretty demanding for even computers now.

I'm curious how different the game would have been if they coded it for 64-bit machines from the ground up? Would it have made much of a difference at the time or now?