One, ID cards aren't going to stop that kind of thing. If they've got all that info then they're essentially you. ((But the Board of Elections checks death records, that's why they have your DoB.))
Two, the Board of Elections sends out voter cards every election to your address of record. Sure, someone could intercept said card at the mailbox but at that point they're playing with USPS regulations, which makes voter fraud look like a speeding ticket.