The individual pays the cost. Today Uber drivers get like 80% of the fare. If Uber needed to pay benefits, give vacation time, etc, the pay rate would be much lower. That would all come out of the 80%. Just like how contract programmers bill a higher rate and get no benefits. Calling someone an employee doesn't suddenly create new money. I can't imagine uber drivers would prefer a lower rate of pay, but hey, I guess…
There's no intrinsic reason Uber's take is fixed at 20% - maybe their business can only viably employ humans (with all of their attendant needs like health insurance) with a smaller take.
Even if you pared Uber's take back to 10%, or 0%, it wouldn't cover the costs of making them employees. And it's the drivers that would take the hit.
Uber provides a tremendous lead-gen service for drivers. Everyone here who's tried to run a business knows that finding customers is the central challenge of a business. Uber completely handles that challenge for drivers, for a risk-free 20%. That's a pretty good deal.