I think I was registered in 3 or 4 locations in Chicago when I left.
There was nothing nefarious about it on the voter's part - you moved and reregistered. I never assumed that I had to let the previous voting location know - I assumed they would take care of it (but they probably never did because it takes time and money to do so and there's no benefit in it). I only found out about it by accident (I don't recall how). It never occurred to me to try to vote multiple times. It's illegal, of course.
Similarly, I've never notified my previous state's board of elections that I moved. I assumed the new state would take care of it.
Now this was 20+ years ago. Maybe things are different now.
It's hard enough to get someone to vote once. Who (except a tiny, tiny fringe) is going to even bother to try to vote twice?
But to your point, yes. The actual cases of in-person double-voting or other types of fraud almost invariably seem to be done by Republicans.
Cheers,
Scott.