Yes, I've seen that list. 1145 instances of fraud over 36 years! That's a whopping 31 cases a year. Few of those cases involved undocumented immigrants voting in elections.
In 2016, there were 123 million votes solely for the Presidential election, not including primary votes. The number of fraudulent votes is something like 0.00002% of the total.
Seriously, dude. That's effectively zero.
*bzzt* wrong. Try again.
First of all, we're not talking exclusively about ID. We're also talking about legitimate voters getting kicked off of registration rolls, and closing polling stations in minority neighborhoods. There is no question that those types of maneuvers discourages or blocks legitimate voters from exercising their rights.
Second, we are talking about cases where legislators deliberately designed laws to disenfranchise voters. E.g. in North Carolina, the legislators actually did research to figure out which types of identifications are most commonly used by whites, which are most commonly used by blacks, and used that to determine which forms of ID the law would require.
Along those lines, there is lots of research that these voter ID laws... wait for it... suppress minority votes. What a surprise. It's not like the US has a long history of disenfranchising minority voters or something.... *COUGH* Jim Crow laws *COUGH*
Third, last I checked there is no federal or state requirement to carry an ID at all times. We don't provide them for free, and they aren't always easy to get.
The reality is that these laws have very little to do with the non-problem of undocumented immigrants voting in elections, and a lot to do with disenfranchising minority voters.