One problem I suspect we'll see is that the sick people most exposed to others won't take sick days, because they don't get paid sick leave.

There are a lot of hourly workers in the service economy that don't get sick time, and they still need to pay their bills. I'm not personally worried about the people in my office since I can avoid close contact. I'm worried about the people stocking shelves at grocery stores and pharmacies, working checkout counters and the like.