I think the primary issue is that Uber provides incentives in the contract for "employee-like" behaviour.
Imagine an extreme case where minimum wage is $8/hour and I'm offering a contracting job that comes out to $0/hour before incentives. If people work 8 hours a day on the schedule I want and do everything else that employees have to do, I give them $4/hour. Now most of my workers will be just as good as employees, but at half minimum wage. They say "I'm working like an employee, I should get minimum wage." I say "They have all the freedom a contractor has, they aren't employees."
Sure, in this scenario there are still people happy to work an hour here and there and earn the $2/hour or whatever it comes out to, but this isn't about whether those people exist or in what proportion. This is about the people who feel compelled by Uber's incentives to treat themselves as employees of Uber without receiving the legally mandated protections and benefits afforded to employees.
This also isn't about supply/demand, the free market, and whether people want to work for that $4/hour or not. The fact that we have minimum wage in the first place is proof that the country has made a decision to not leave employment terms to natural equilibria.