I'm pretty sure randomizing supply tiles has been tried a number of times, if only because people have often thought that was the correct rule. I don't think it would break anything, per se, but it would prevent you from planning ahead as carefully (knowing when that interest payment is due is pretty important early on) and add a bit more chaos/luck.
LOL! I just played this weekend (for the 6th time) and just discovered the rule that you do NOT randomize each round. Yep, I was one of them you note.
Ahhhhh! Made it much easier to plan.