Over an act the SCOTUS will find invariably unconstitutional, btw... 
??? Not so sure about SCOTUS finding it unconstitutional, if that were the case, having to show ID to obtain a driver's license, obtain medical care, apply for a mortgage, open a bank account, etc., etc., would be unconstitutional. Also one needs to provide a birth certificate (proof of citizenship) in order to obtain a social security card.
Having to show proof of citizenship in order to get a voter ID is NOT unreasonable and follows the same premise as having to use ID in the other instances that I mentioned.
This isn't one of Trump's brainstorms but he is giving his base one of the logical cases that they have made against ILLEGALS voting. Secondly, it is helping to ensure that, that avenue of fraudulent voting is shutdown.