What I see in the streets of another European city in a country with a long history of discrimination against Roma people is a lot of Roma beggars. But these are very clearly not local people. They seem to be Romanian and working for an organised ring. If the situation in Denmark is similar and if the laws are targeted against exploitation of disadvantaged people for begging then that would be acceptable (and if not ECHR will have the last word on that).
They actually already did. Dian v Denmark. Ruling that the ban wasn't illegal.
I had my passport lifted by a pickpocket while at a restaurant in Vesterbro and had to report it to the police and then go to my embassy to get a replacement. Both the Danish police and the US state department employees were amazing.
I'm not a Dane but have spent significant time there and well understand the spectrum of views Danes hold on immigration and Danish politics in general.
I wasn't even passing any kind of judgment, but bringing this up because DHH was discussing a topic that comes up locally (even though he doesn't even live there anymore) but sounds crazy if you don't have the context.