I agree that seems infeasible that wouldn't allow Americans to come home - I don't think any of the travel restrictions in countries block their own citizens coming back home, albeit into quarantine / self isolation, which I think is also the case here.

I think Trump's announcement itself had issues, in suggesting that commerce would also be blocked, causing confusion.

Couple of things that surprised me:

Doing it now, after the virus seems to have become community spread in the USA, rather than a bit earlier - certainly put restrictions on China quickly, which I think was fair, but seemed slower to put them on Europe until almost too late. Certainly not alone in that - I'm pretty sure I read somewhere about a country that had two confirmed cases of Coronavirus, that came from America, so they put travel restrictions in place, but only on Europe which seemed a bit funny.

Not including UK / Ireland to begin with, given reasonably open borders to Europe, plus Britain's apparent desire to go for herd immunity, and thus to let the virus spread in the UK, which meant that if not wanting to follow suit, would want to include blocking the UK as well.

Living in NZ, we have put some pretty heavy restrictions in place now, though remains to be seen how well we can enforce it, but at least this early in the piece seems to make sense to try and block all countries, but again, many countries seemed to be slow to react, and thus have to react strongly when they do.

Regarding the seasonality of flu, certainly could be the case, and let's hope so, though could come back next winter, but I think it seemed to be part of Trump generally downplaying the threat, saying not likely to do much to America, until it has suddenly exploded - I think if he had presented a view of it being more serious, then potentially there may have been more upfront action to try and mitigate things further.