Because the express intent of those laws has nothing to do with the integrity of the system and everything to do with the Republican party's desire to limit voter turnout. By your same logic, if Republicans are so concerned about voter integrity then why aren't they pushing to include everyone's vote?
Who's vote are they trying to exclude? You have to show I'd at the bank. You need an I'd to drive a car. You need I'd to get a book at the library. Who's vote are they limiting by having people prove they are eligible to vote?
http://www.washingtonpost.com/news/...le-incidents-out-of-one-billion-ballots-cast/ So 31 cases of voter fraud out of a billion votes cast and you want to look me in the eye and tell me that we have a problem with voter integrity? Bull shit, Bengal. My point is that there is nothing wrong with the existing system before all of these voter ID laws. If we had issues with voter integrity then I'd be more apt to listen to your reasoning, but the argument you are trying to make is moot because there was never an issue with voter integrity to begin with.
31 out of the last billion votes cast were proven cases of voter fraud. We do not have a problem with voter integrity. The Republicans have a problem because their ideas do not support a majority of the voting public any longer. So in order to limit the number of people voting, they've passed these draconian voter ID laws to make it more difficult for the least of us to vote.
Voter ID cards have always served as one's voter ID. You only get one of those by registering to vote. In turn, when a person registers to vote their name is added to the roll of eligible voters in their district. Over the past 1 billion votes that have been cast, we've had 31 proven cases of voter fraud. So to answer your very rhetorical question, we already have a means of identifying who are eligible voters and who are not. If you can name me one election that would have been swayed by 31 votes then maybe I'll listen, but you cannot because such an election has never happened in the history of US politics (federal level). Furthermore, if you dig a little deeper you will see that the vast majority of those 31 cases involved mail-in ballots and not voters who stood in line and voted on election day.