Can you give me examples of European countries where there are no forms of ID that are free and accepted at the polls?
The US doesn't require citizens to have ID to exist. That's part of "freedom" in America (I mean this genuinely).
So it is an additional step if you want to vote. Cynical state governments have tried to shape who can vote for them by making IDs mandatory and strategically closing ID offices in certain areas, reducing office hours (among other barriers). It's not a hypothetical situation.