Does anyone see this breaking the game or giving one player an advantage over another?
Yes, it breaks the game...or at least breaks the game as it was intended to be by the designer.
Simply put, each player should accomplish both phases before moving on to the next player, because one player's Building Phase needs to be informed by the previous players' Command Phase. Simple as that.
BTW, if you do a search, or simply go back a few months, you'll find many threads on this exact topic where this same discussion has been exhausted. You might find some great tidbits for you to consider, in those threads!