So this gets to the heart of the question, do you have the right to drive? yeah absolutely. Just not on public roads. The reason you need a license is to use roads paid for by taxpayer money. Maybe another question that needs to be asked, is does any agency have the right to tax me for building a road, then not allow me to use it? Rhetorical question maybe but its worth thinking about.
I agree with you though. I actually tend to support some kind of process to help verify ID's. This may be a good idea, or it may not. Only time will tell nobody knows, but I tend to think its a good thing.
Then, using that logic, it would be perfectly lawful, just, moral, and within the authority of the government to require a license for walking on the sidewalk, or riding a bike on the road, or using 'public property' in any way whatsoever, parks etc. This would include buying water or any commodity from a public utility, or requiring virtually anything they desired in order to attend public school.