Voter fraud can happen, and it is not even that difficult. With elections finishing with a winning margin of less then a dozen votes, it would not take much to end up with an illegitimate winner.
Requiring voters to show ID, while no where near full proof, does increase the burden significantly on fraudulent voting. Having a simple protection, such as sealing the ballets of those who can not produce an ID to allow for a final purge of the voter rolls of the illegitimate names and in the event two or more people claim the same identity would ensure that people would not lose the right to vote if that vote was legitimate.
Video embedded below.