I have zero problem with this. I'm not so sure why it's so hard for some to just come out and offer a solution.

It's not. As noted upthread, progressive lawmakers have introduced a bill to provide a national ID card for people who need one. It appears it's been introduced in the last several Congresses. It fails each time.

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I think you're overly optimistic in your assessment that such a bill would be welcomed on the GOP side of the aisle. Partially that's because it would require the federal government to spend money to provide people with ID's, and there's a general dislike of increasing government spending on almost anything. DOGE, and all that - but Grover Norquist was here long before Musk. I suspect that the "small government" types who fear the idea of any national ID have also torpedoed this proposal - even apart from the spending, they distrust federal government programs, and certainly don't want the feds to be in charge of doing something like this.

If everyone had an ID, it's unlikely Democrats would care. Again, few on the Democratic side believe that there's any material in-person fraudulent voting going on. Voter fraud sometimes happens (at very modest levels), but it almost never involves a person showing up to in-person voting and pretending to be someone else. Democrats generally think the only effect these laws have is keeping legal people from voting. If everyone had an ID Democratic opposition would vanish. But if everyone had an ID then there would no longer be much benefit to the GOP to enacting these kinds of laws, so there's that....