This would also apply to the US sherrif on vacation.

And this would also create an incredibly dangerous situation for everybody.

The Us cop would act according to his own (non-German) training and daily routine, which includes lots of violence that he uses (because he would have the right to do this at home) on the suspected person and maybe on other persons standing in his way. The US cop would also expect and fear violent reactions. But people would react very differently. He would surely misread most people’s reactions and then probably escalate his violence far too much, and far beyond all that is allowed for such an “everybody detainment”. In the end he could be the only one charged with crime, and pay for many people’s hospital bills.