I do think advising people who had been to Northern Italy to stay home for 2 weeks might have been sensible. I do think schools are getting conflicting advice re this. In the school where I teach, one family went on holiday to Northern Italy, near but not in one of the hotspot areas. The advice was for these children to stay home for 2 weeks. However, for larger school groups, the advice is that they should attend school, unless they are showing symptoms. IMO, if any students start showing symptoms, it'll be too late as they could have already spread the virus to several people. We're talking about students who are mostly old enough to stay home alone, and a relatively small number of teachers.
From the way there was a sudden jump in cases in Italy, I think it's clear the virus was being spread to a lot of people before it was detected. Before this, I wasn't too worried, but now it does feel like similar outbreaks could happen in any European country, and our government seems not to be taking things as seriously as it could.
It would be really simple to e.g. advise against travel to all of Northern Italy, and allow people to get money back on holidays! I'd also consider advising against travel to affected regions in Germany.
I do think these are all things that could be easily done, without much economic impact, and without causing panic, but are sensible precautions.