Assuring the integrity of the voting process is something that most citizens instinctively understand is the right thing to do. In the America of 2012, you need a picture ID to get on a plane, ride Amtrak, open a bank account, perform any transaction with most businesses and government, as well as buy alcohol or tobacco.
Why is voting less important? States must preserve the integrity of the ballot process, especially in an era of close elections. Given the potential for long, disputed outcomes (Florida in 2000 and several state elections since then), there is a need for zero tolerance in voting fraud.