We should all care. Uber doesn't provide health insurance. Instead Uber drivers get their healthcare costs covered by the rest of us (either via ACA subsidies or written-off care provided to the uninsured).
Besides, what you are actually stating is that Uber riders should pay for Uber driver's health insurance, rather than the general population.
Ideally health insurance should be decoupled from employment status, but until then, we should all play by the same rules.
(This seems to be more about minimum wage, workers comp, UI, etc. which they would get)
So what? People without jobs also get their healthcare covered by MediCal (with zero out of pocket expenses). Is that also a problem? Wouldn't it be better if we had universal healthcare?
And we subsidize employer-provided healthcare also, hence its existence.