Trump falsely claimed the 2020 election was stolen, and then he tried to steal that election himself, and is now trying to steal future elections. US democracy is under threat.
If you are disenfranchising millions of Americans to stop a few dozen potential illegal voters, then your goals are to make it harder to vote, rather than to secure the election, unless you are just ignorant of the facts.
Kansas tried a documentary proof of citizenship law in 2011 and it blocked 31,000 citizens from voting–12% of first time registrants.
The founders intentionally did not give the president the power to regulate elections because they feared something like a king or a dictator. Yet, Trump is claiming such powers.