A lot of people will simply lose their jobs if they don't go in to work, whether they're sick or not. A lot of those jobs are in food service. Wearing masks in extremely crowded public areas going forward is probably a good idea.
It depends. You are right that if you can work from home, you definitely should, if infected. But we cannot expect people to be quarantined because of a cold, you might have to buy groceries for example. Or travel to a doctor. Or if you have to come to work. In those cases, wear a mask!
There are simply situations where people are sick but still need to be out in the public. For example, if you are sick but your child still needs to be taken a school event or needs something from the store, you may still need to go out in public.
Ideally, people who are stick will stay home, rather than put on a mask and go out into public. However the current state (pre-pandemic) is 'be sick, go out into public and claim it's just allergies'. So perhaps putting a mask on is a good substitute.