Licensing is partly to assure responsibility and partly to control the masses. Lacking a license does not deprive you of the right to travel, as you can walk, bike or take a bus or train; and I can find no constitutional right to travel conveniently!
Read the text of the bill summary and the points it makes. There is no "convenience" in automobile travel in modern day America - about a handful of cities would provide one to live without extensive use of an automobile. Revoking said right is essentially revoking the right of an individual to make a living.
Furthermore, as the summary provides, the Articles of Confederation incorporated a similar Right to Travel, but was dropped in the Constitution as it was considered too obvious to require. We hear similar stories of those arguing against any of the Bill of Rights, including the 2nd. It is more than fortunate that our founding fathers did incorporate the text that they did in the Bill of Rights - the statists would claim similarly that owning a gun is a privilege.
I live in GA, working near Atlanta.
Short response: if you don’t drive, you can’t function here.
Walking or biking any meaningful distance and frequency will get you run over. Really.
Buses are too far and infrequent. Trains are worse. Both require you pay; no money, no travel (think “poll tax” for your argument).
Existing driver licensing is too lax to warrant existence of such regulation.
There is no compelling reason to treat driving as a privilege. To the contrary, in modern society it is as much a right as buying food (”you could grow your own...” arguments are just as inane).
Actually licensing does not restrict your right to drive. It restricts where you may drive. You do not need license to drive on private property. You need a license to drive on government owned roads. The government is basically regulating the use of government resources. It is hard to see a constitutional issue in that.