As to non-citizens voting, I have not heard anyone suggest that is good or right. Including those opposed to the current SAVE bill.
But everything in life is a tradeoff. The argument against the SAVE act boils down to 2 things: 1) there has never been enough illegal voting to even come close to swaying an election and 2) the provisions in the SAVE act would make it more difficult for many legal voters to exercise their right to vote. People may disagree about how difficult it will make it but it will make it more difficult.
I don't see an issue with voter ID. But the ID required can't be so restrictive that it unnecessarily excludes too many legal voters. Much has been made online that we require a DL as ID for many daily activities. But a basic DL does not allow you to vote under the SAVE act. Even Texas doesn't not require ID anywhere as restrictive as the SAVE act (
https://www.votetexas.gov/voting/need-id.html).
As to a national registry of eligible voters and/or providing voting roles to the federal government, think about it. You are giving every administration the opportunity to choose which voters are eligible to vote. That's like giving the fox the master key to every henhouse.
Personally, I'd love to see an independent forensic analysis of a prior election. But I don't see how it could happen and still maintain the privacy of the voter. However, perhaps we could audit mail ballots to see how many are not really eligible to vote without looking at who they voted for.
I've read the Heritage Foundation paper on illegal voting; it's instructive to note that there were no examples of mass voter fraud - just a number of small cases. And also take a look at charges/convictions for voter fraud in states where the Secretary of State (typically the one responsible for prosecuting voter fraud) is a Republican. I think you'll find relatively few cases.
Real life abhors absolutes. We can't make voting 100% secure without making it very, very difficult for a significant number of legal voters.