If I (salaried) take a sick day, I get paid the same amount from the same source; there’s next-to-no economic incentive for me to risk the health of others by working when sick: problem is solved.

We could more or less force the same by law for scheduled hourly workers. It’s a little more difficult for gig. It’s basically impossible (as I see it) to put self-employed people at the same outcome as if they worked without substantial risks of under-comping some and over-comping others.