It's probably really difficult to get a super accurate number, but here's what the research says, at least:
'Also, you don't need an ID to buy cereal'
checkyourfact.com
Brennan Center's 11% estimate is probably way too high, but even if it's only, say, 1% of the voting-eligible population, you're talking about 2+ million people. How often do you suppose people show up at the polls pretending to be someone they're not or trying to vote twice? I bet it's several orders of magnitude less than 2 million. It's
less common than being struck by lightning, at least in Texas, where there were 4 cases of confirmed in-person voter fraud between 2000 and 2014. Even if for every person that got caught there were 100 that got away with it, you're talking about 400 votes over the course of 14 years, a fraud rate of .0005% based on the 72 million ballots cast in Texas during that time frame.
So, do we prevent 2 million people from voting to protect against something that just doesn't happen? Which would be more likely to change the election results, MAYBE a few dozen fraudulent votes that we don't catch or, say 250,000 people prevented from voting because they don't have proper ID (if only 25% of those without ID even want to vote)?
It's easy to say that those people should just go get an ID, but if they cost money, a poor person might understandably save their money for necessities, if they require proof of residence (ie. utility bills and whatnot) a homeless person can't get one. Some may not have transportation to get to the location to get one, some may not be able to afford to take off work to spend the time to go get one. There are
many reasons why someone may not have an ID that could be used for voting (including, ridiculously, a misspelling on one's birth certificate), and it's not always the most convenient task to get one.