If votes weren't anonymous, maybe. But they are.

Wait, you're assuming anonymity and the ability to "decide later if my vote was valid or not"? How would that work?

The process will vary by jurisdiction, but one approach is to identify if a voter has questionable eligibility when they arrive to the polling place, allow them to fill out a ballot, have them seal it in an envelope, and then label the envelope with the voter's information. You can then take the time to verify the votes validity before the envelope is reopened and the ballot is counted with the other votes. And just like with traditional ballots you can have the process observed by representatives of multiple candidates/political parties to ensure both transparency and that no vote is maliciously discarded.

Oh I see. That makes sense if you can get the government to use paper ballots everywhere (best of luck in the US). It does make me wonder how well it would work out in practice though. If verification happens at the same time as the vote, then you can try to correct any issues that come up right then. (Maybe bring additional documentation right then? I don't know.) Whereas if you introduce a delay in between... how many people are actually going to go through the hassle of dealing with it later (especially imagine having to take days off work) to work through the legal bureaucracy and have their votes counted? I feel in the US it seems a little bit too optimistic that it would work out fine, but maybe I'm just pessimistic...

There is zero reason a voter can’t be given a provisional paper ballot in a jurisdiction with electronic ballots.

You don’t want to verify eligibility before voting because it slows the process down. The longer it takes to vote, the fewer people vote. You just collect the voter’s information and then the responsibility for the rest of the verification is on the government. It occupies the government’s time to verify the vote and not the voter’s time.