In order to implement something like that, you'd need to rank awards from most important to least important, and it's possible that every nominated game would have been disqualified for the later awards. There's basically no way to prevent multiple awards going to a single game with a rule.

The difference between the Steam Awards and the VGA is that the VGA is a bunch of industry insiders who voted, so there's a risk people will discuss their votes beforehand with each other, leading to bandwagoning.