I'm not taking a position on its legality. In most cases that's undefined because the law did not anticipate this situation and it's never been tested in court.

They obviously can't prohibit people from checking emails or taking work calls while on vacation, because that means the end of big-spending tourists.

Nobody has drawn a red line at a magic point along the continuum from one emergency work call during a two-week holiday, to 9 hours a day in a hotel room hunched over a computer. Where would it be, and why does that particular point maximize benefit for the host country?

This is not how the US judicial system works. We are innocent until proven guilty. In the case above, to say it is illegal even though it was not proven violates the above. Also, many “laws” aren’t technically codified but instead have been established by precedent, and no precedent is hard and fast. Technically you could argue both the things you mentioned above in court and win, rendering your actions legal.

We're not talking about the US judicial system here.

And your statement is nonsense, murdering someone is illegal whether it's proven or not.

There is a difference between de jure and de facto.

Defacto, going 61mph in a 60 is legal practically everywhere. De jure, it's not (the law is on the books).

Same as jaywalking. It's more of a law to pass responsibility in an accident (i.e. if you were jaywalking and got hit by a motor vehicle - you are at fault because of jaywalking. Jaywalking itself is very rarely prosecuted as a standalone thing)