This sounds made up but limiting access to “free” services is not unheard of. This topic has been litigated to death. There are no new arguments. If you are in favor of voter ID laws you are simply ignorant.
[1] (Though mass disenfranchisement is almost certainly the actual purpose of the law, not security.)
If they can't put up some minimal effort, what was their vote worth? I don't think the laziest folks probably vote in good policy.
I'm not worried about lazy people voting. I'm worried about crazy people voting, and not having enough votes from sensible people to drown them out.