So why didn't your uncle simply get his driver's license back when he was 16? They should have solved the problem in the previous generation!
The only way this matters is if the percentage of people sharing your cousin's circumstances is large or increasing, and I see no reason to believe that's the case. It's not as if these requirements are new, after all.
Furthermore, I suspect that in the vast majority of cases where the parent lacks a license, it's because the family lives somewhere like Manhattan where the child doesn't actually need one either.
In other words, this is a non-issue that you only think is important because one of the tiny number of people who are affected by it happens to be somebody close to you.
So should parents be held responsible for driver's education of their children in the same way that they are held responsible for the child getting to school and back? For example, should it be considered neglect on the parent's part to either A. not hold a driver's license or B. not take the child out for practice driving?
No, I'm saying it's not the State's responsibility to let unqualified people have drivers' licenses just because their parents couldn't be bothered to teach them, or to subsidize their parents' fuck-up!
And by the way, "resort[ing] to paying $50 per hour for a driving instructor" is a false dichotomy: just because your uncle can't/won't help, doesn't mean that's the only other choice. What about your aunt; can't he drive with her? What about your cousin's uncle (i.e., your dad)? What about over-25 family friends? What about a random neighbor, who is not an "instructor" and therefore probably would charge much less than $50/hour? What about you?