Not all European states provide free IDs, and some US states which require IDs provide them for free.
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.