Tests are not free, not 100% accurate, and not 100% available. The doctor you called stupid is in control of exactly 0 of those factors, and has no effect on europes policy.
If my health care provider can try to sell me antibiotics despite a negative strep test, "just to be sure, because sometimes you get a false negative", then they're surely not ignorant of the phenomenon where tests are less than 100% accurate. (Perhaps they're just variably aware of it, depending on what the bean counters from the health care network's corporate office are telling them to do. But still.) And, if you take a "better safe than sorry" attitude regarding false negatives, then you're not too far off from realizing that not having the test is not that big of a deal, because you'd be telling people to stay home when they're sick in either case.
This is a viral illness. There is simply no treatment. You go home, rest and eventually get through it in most cases. If you have annoying symptoms, you try to alleviate those in the usual ways (as if it was any other cold/flu). If you get life-threatening symptomps, you call for help and they'll take you to the hospital (at least while they aren't completely collapsed).
What would you like the doctor to say or do here?
Specifically, I would like the doctor to say, "Stay the eff home and keep your germs to yourself, sickie."
More doctors doing this would also help put pressure on employers to change their policies. Maybe (dare I dream?) we can even get restaurants to start giving their employees sick leave, and encouraging them to use it, instead of requiring them to show up and germ up all the food on pain of losing their jobs.
Yet the doctor is one of many who are dismissing the likelihood of somebody having coronavirus just because they haven't been to Italy. So yes, stupid.
Now the infected population is very small, so if too many non infected people is testes, the false positives would be much bigger than the true positives. So you would get a lot of people unnecessary in the hospital while they have a normal cold or flu.
Anyway, if the symptoms of a normal cold or flu are so bad that deserve hospitalization, the doctor will send you to the hospital even if it is not covid19.
[If you are in a risk group, get the flu vaccine. It will not protect you from covid19, but you definitively don't want to catch a bad flu while the hospital if full of covid19 patients.]
The amount of infected people calling in who havent traveled is _infinitecimal_. The doctor saying you're not infected is correct an OVERWHELMING amount of the time, probably >99% accuracy. Eventually, this wont be true, but then the doctor wont be telling everyone to go away because theyre not stupid.
Now, if you want to argue the merits of extreme overcaution and attempting things like 100% testing for a global pandemic mitigation plan, good for you. You have a lot of hurdles to overcome, some of which you named yourself, but none of them are the doctors fault. You are simply wrong.