Thanks for the context.
He’s speaking to evangelical Christians that do not regularly vote, and in the context of instituting voter ID to secure future elections.
ID is required to vote in most (all?) EU states.
I think you’re being disingenuous and deliberately trying to refocus the conversation on something else now.
He literally said “if you vote for me, you won’t need to vote again”. It’s not an ambiguous statement and doesn’t require extra context. Everything else you said didn’t really have anything to do with it.
The issue with voter ID laws isn't with the concept of having to identify yourself at the ballot box, it is with the way it is implemented.
For example, in my EU country I can vote with my passport, my drivers license, or my ID card, and they accept documents which are expired for up to 5 years. For context: this is less restrictive than the documents anyone is technically required to carry every time they leave their home! The number of people who can't meet this requirement is basically zero, and a decent bunch of municipalities offer them for free to poor people.
Meanwhile US has no universal ID system, which allows the pro voter ID groups to carve out a list of "acceptable" IDs which just so happens to be popular with the people that are going to vote for one side of the political spectrum, while excluding the forms of ID which are popular with the other side. And of course it's not just about identification, as they also add a bunch of irrelevant details to the requirements like the information having to exactly match your birth certificate.
Combine that with the failed two-party system where even a handful of votes often completely swings the political landscape and it is pretty obvious what is going on.