It's hardly proof of address. At best, I'd say it's proof of state residency.

I've moved several times since getting my Colorado driver's license (a REAL ID). Technically, you are supposed to submit a change-of-address form to the DMV online within 30 days of moving. They don't send you a new card when you do that; the official procedure is to stick a piece of paper with your new address written on it to your existing ID yourself, and then just wait until your next renewal to actually get a card with the new address on it. The change of address form does not require utility bills or any other proof of the new address-- that's only required when you initially get the driver's license.