Birth certificates do not have photos.
You make a valid point about resident aliens, green card holders, etc. who can legally obtain drivers licenses. Yes, they should be able to obtain such licenses, however it should be stamped clearly on the license that the holder is NOT a U.S. resident. Many states issue licenses that have such a stamp in red lettering or similar that states that a minor is under the age of 21 and such. It is not a new thing. Either that, or states must issue a separate voter ID which includes a photo.
I should have known it was not an original idea.