You need an ID to drive, buy alcohol, buy cigarettes, board a plane. And people manage to do all those things.
Actually you need a REAL ID to board a plane now. 20% of americans don't have them. They're pointless, take a lot of time and effort to aquire and are needlessly expensive.
I don't have one because I have a passport.
In much of Europe you don't need ID for those, except a driving license, which happens to be an ID but primarily exists to prove you are qualified to drive. If you look young you are asked to prove your age if buying cigarettes or alcohol but the requirements for that are relatively low.
Until recently in the UK you did not need any ID to vote, that was introduced recently as an echo to the US stolen election conspiracy, as demagogues love to steal ideas from each other.
No, all people do not manage to do those things (even if they wanted to).
You can do all that with a driving license, but a driving license is not a proof of citizenship and thus of your eligibility to vote.
In Europe, you can't get a regular ID without being a citizen. So having an ID automatically means you're eligible to vote.