Unfortunately the US is setup in such a way so that individual states get to decide who is eligible to vote. This is a state right defined in the constitution[0].

In practice the vast majority of states have similar voting requirements. But because, in theory, they could all differ then no unified automated system is possible, it would have to be per-state.

Of course individual states could create an automatic voter registration system, and I believe some have/do. But a lot of other states are actively trying to disenfranchise the poor, young, or minorities who would benefit the most from automatic registration.

Ultimately voting and voter registration needs to be handled by a non-partisan organisation within states. But considering it would take partisan politicians to set up such a non-partisan organisation, it has little chance of happening.

[0] http://blog.constitutioncenter.org/2014/08/constitution-chec...