My family made a trip to E. Asia last summer, so we had a small supply of masks available since it was quite normal to wear them in public over there. In fact when we came back to the US we arrived fully masked. We were stopped at customs processing saying we were in the wrong line, until I showed all our blue US passports!A major reason for those recommendations is probably the fact that we have a severe mask shortage relative to those countries and that, as Beagledog said above, our healthcare workers don't have enough of them. This is not a matter of wanting to protect healthcare workers for the sake of protecting healthcare workers. We want to protect them so they can keep working to protect others.
Korea, China, and other countries in Asia have a couple major differences from the US: 1) They make more masks in those countries and can choose what percentage to export. 2) They had significant experiences with SARS and MERS which helped them to be more ready for this pandemic.
I agree with you that if we had enough masks, it would be great for everyone to wear masks when out (in addition to staying home if sick and as much as possible otherwise).
Here's a FB post I made the other day saying much the same thing:
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I understand there's a shortage, but I'm seeing quite a bit of mask shaming going around instead of trying to normalize their usage. Just this weekend I saw families having playdates with their kids, young people still congregating in groups and others just going about their business as if nothing has happened. No one wearing masks or taking preventative measures seriously.