I don't think this is known or knowable at the moment. Hence the worry.
You are right that airports are probably a greater risk. Perhaps they should be closed. On the other hand, that would be far more disruptive.
As for basic hygiene, yes, we all should. At the same time, we all know that a significant fraction of the population can't or won't do this.
Edit: Here's the proper method: https://www.who.int/gpsc/clean_hands_protection/en/
A significant caveat is that the sink/restroom must allow proper handwashing. Many lack paper towels, for example. If you have to touch the faucet handle or the door after you start washing (which takes two minutes), the method has not been followed. It's harder than it looks.