Just like we need to protect the 12 year old who voluntary enters a coal mine, we might need to protect the Uber driver who voluntary gets into their car.
By "protect" you seem to suggest "outlaw the thing they want to do".
Can you imagine how outraged you'd feel, to be treated the way you're suggesting treating others?
How would you like for the state to say:
"Hey, /u/slg, for your own protection, you're not allowed to eat sugar anymore. It is now illegal to buy and sell sugar. You'll be fined if you try to purchase sugar, and if you're found with sugar in your house, you'll be taken to jail. These threats are, of course, for your protection, as the harmful effects of sugar are well-established."
I don't personally agree with the US's war on drugs for example. There is probably an argument that on total sugar is more damaging to American society than marijuana. If society decided to ban sugar, I wouldn't be thrilled, but I would understand it.
This isn't a win for small government.
If not, then the problem with Uber isn't the part-time-ness, and forcing the job to be full time is a very awkward way to try to fix the exploitation.