I think that's a reasonable solution. The problem would be that the AI would probably be crippled by it.
If you could mod the game so that it only happened to the human player, I think it would work.

I just started a new campaign as Rome the other day. My current plan is to train cohorts only in Rome - all other provinces will have an auxiliary barracks.
I'll make a half stack in Rome and then move to another province with an auxiliary barracks and fill out the stack. It wont do anything about replenishment but I think it'll make the campaign more interesting.