You are right, and I want to add more perspective that in your proposal there are now 2 cars on the road. Your electric and your used ICE car. The better situation is to drive your ICE car to its end, and only then replace it.
Our over consumption is a part of the problem as well.
If half of the world immediately upgraded to electric cars, sure there would be a temporary surplus of vehicles, but it would only last until the old ones broke down.
Exactly. There'd be a temporary surplus of (newer, better-condition) ICE vehicles. And people who are otherwise faced with a $1500 bill to repair their old one "kinda needs repairs, burns some oil but a quart a week isnt too bad", will instead buy a more efficient ICE. Most new BEV will get an old shitty ICE off the road.