One supposes what they'd really like is to be able to enjoy both flexible hours and typical benefits and worker protections. Unfortunately, we've set up our stupid system so that these are somehow exclusive.
The reason a lot of Uber drivers don't mind being contractors is because they already have full-time jobs that provide health insurance. But ask drivers who drive during regular business hours (they will be more likely to not have any other job) and they will probably tell you that they would rather be employees.
I guess one other way these things are exclusive is that they drive up costs for sharing economy companies. Some of these companies are pricing so low that they are barely making a profit as it is. If their costs are even higher, they will have to drive up prices, and at least part of their appeal immediately vanishes. At least a few of the companies will die if that happens.
I wish people would realize this is a morally neutral outcome. Like, oh no, another company down the drain. It's not like they're a limited resource. We should be willing to sacrifice a thousand companies if they can't succeed on the profit metric under the rules we've set.
"Sharing economy" type companies are a good idea. They'll succeed, or better ones will. They don't need coddling.
If you want a libertarian paradise where government doesn't interfere, move to Somalia.