I suppose this depends on the state. California driver's license numbers don't change, even if you move away, get a different one, then come back years later and get one back in California.
Yeah but while you're in a different state your "current driver's license" is the one from that state. Effectively it changes when you move, and changes again when you go back.
True, it changes back to the old number when you go back. But as you move from state to state your DL# will change as well.
The Congress could use its constitutional authority over weights & measures to prescribe a national system of ID numbers, administered by the states, with assignment at birth.
But OMG! The government is tracking me! I have freedoms!