I agree with you and I’ve made the same observation but I don’t think it’s due to some misplaced sense of superiority.
I think it’s simply because it has been a while since disease and pestilence was a worry for the average Western country so the average citizen (and therefore the leaders) are complacent in a sort of “It can’t happen here” way. There have been outbreaks such as the AIDS epidemic or swine flu but nothing as impactful, infectious, and at the scale of COVID.
Whereas Asian countries have grappled with issues of SARS, Malaria, AIDS, Polio, and many more in the not so distant past and have learned the importance of taking public health seriously. The experience of the outcome of mismanaging a response to a previous epidemic is still “fresh” so to say in many of these countries. I think a good example of this is how South Korea dealt with SARS and evolved their response to COVID based on the learnings from that.
Lastly I wonder if the prevalence of more communal societies in Asian cultures make a difference. I can imagine it could make the problem worse but it could also be beneficial in the sense of providing strong societal pressures to quarantine/hand wash/social distance/etc.
Edit: And of course the misguided leaders in particular Western countries are not helping. Maybe the US this particular time is just a statistical outlier due to some mismanagement and there is nothing more to read into further than that?