I’m sure it has worked at least once. There’s no guarantee it will work 100% of the time and is a problem. its up to the individual states to ensure this and not every state does so.
when i registered in the new county & state, I certified I wanted to be removed from the old county & state. That never happened. I filled out the appropriate paperwork 3 times and mailed it in. I am still a registered voter in two different states after trying 4 times, 2 in the past 8 months.
as a pillar of democracy, it should as close to perfect as possible. It’s broken and needs to be fixed.