Right? That's a ludicrous assertion. Here's what's required to move somewhere else within the US:

1. Move.

At some point, you have to get a new driver's license in your new state and transfer your car registration there to use their license plate instead of your old state's. Those are "mechanical" paperwork transactions, though. You show up at the Department of Motor Vehicles with proof of your new address and they scowl at you and then issue the new one. You don't have to ask permission: so long as you meet the local requirements to do those things (like pass the local driving test, have a car that passes the appropriate inspections), and have the right paperwork (like proof of address, proof of ownership of the car, etc.), you'll get it. And that's the "hard" part.

I've moved between states multiple times. With the sole exception of car-related stuff, the only difference between moving between a different apartment in the same complex and moving across the country is that you have to pay your taxes somewhere different the next year.

having moved often for the military -- it's not trivial. and I had the military paying to schlep my stuff and was single + no kids.

but it is easier than Europe would be, for sure. yeah there is free movement but often wildly different language, customs, and processes.

meanwhile there is WellsFargo, Safeway, and a DMV office in WA and MD

oops! Now I read it... reads totally backwards. I meant, moving state is easier as moving between countries in the EU