I don't quite agree with automatic registration, but would happily accept making government-issued IDs free and automatic. Hell, pair it with the draft registration and make it a required DMV visit, for everyone including women.
One big "You are an adult, now here is the start of your adult life. Come to the DMV, we will give you your ID, run you through the selective service, and if you want sign you up for voter registration."
And then anytime you need to renew your ID, also renew registration.
There, we both reach a good compromise, that streamlines a few processes, and ensures nobody is left out of a legitimate process. While also ensuring voter rolls remain clean every ten years.
Addition: Fuck, I'd even advocate adding a required single class on basic American civics and responsibilities. Completely free, make it a legally exempted day like Jury duty is for things like work and school. You go in, get a rundown of your rights and responsibilities as an adult, sign all your paperwork, get your ID, and leave as a full and functional adult of the USA.