Texas does just that! When you apply for a driver's license or other state ID, you can elect to register to vote at the same time. Two birds, one stone.
Texas is hardly unique in this, since every state except those which continuously since 1994 have either not required registration or offered election day registration is required to do this under the federal National Voter Registration Act of 1993 (the “motor voter” law.)
Would be nice, but most states do not allow same day registration (New York does not as an example), or same day registration is extremely limited (in California you need your ID to vote and register on the same day).
The aforementioned problem persists, different organizations with different scopes.
Stronger voter ID laws are nice too, until the political will was expended into making it happen. By the same token, smarter ID laws can also be enacted if appropriate effort is undertaken.
Stronger voter ID laws are not nice to haves, they are the law in many states like Texas. Just like anything else surrounding government and laws, you must plan accordingly, appropriate effort is required by the voter.
Since many states don't allow registration on the same day as voting, I'd say the government has planned accordingly after passing the aforementioned voter ID laws. Just found out this is a a standard federally: https://news.ycombinator.com/item?id=41921184
https://en.m.wikipedia.org/wiki/National_Voter_Registration_...