Well it comes down to personal choice in the end. You choose to use ID because you don't want anyone having your personal information, and you already carry an ID. But there are many other people who are just as adamant against carrying an ID, as you are about people keeping tabs on you. It has nothing to do with laziness on either side. Some people think an ID is the mark of the beast and flat out refuse to have one. You may think they're nuts. Just remember that some others probably think you're nuts for worrying about the government keeping tabs on you. And then there are the others who just physically shouldn't be burdened with the process of getting an ID (like the 90 year old ladies). In the end, none of them should be denied their right to vote just because someone else thinks their beliefs are stupid or they're too lazy or whatever.
I'm fine with people proving their identity before they can vote. Where I disagree is when that proof is limited to only 1 specific way that is considered acceptable, when there are several alternative ways that are currently in use today.
I have met people like that and they (from my experience interacting with them) are more against government control of any kind (which includes IDs and your database). If that is the case then good for them. However if they are unwilling to follow the rules society has established and they lose out on priviliges/rights (depends on what we are talking about) as a result then they have no one to blame but themselves.
Edit: I am not paranoid about the government keeping tabs on me. I work for "the man" if you will. However there is no valid reason, in my opinion, for another agency (that is what it would take - or a dramatic redirection of an existing agency database) having my info. There are already enough.