Fair point.Do your citizens trust your government?
The Danish foreign ministry published revised travel recommendations today, reducing most of th EU27 countries to yellow (ie. you can travel there, but pay attention to local restrictions and follow the usual guidelines). The countries that remains orange (ie. travel restrictions apply) are Romania, Portugal, UK, Ireland, Malta and Sweden (with the exception of the Norrbotten region).
The expectations is that the list will be updated once per week to reflect the current infection situation, and should a country go back to orange/red, travellers are advised to end their travel immediately, return to Denmark, and be tested.
The updated travel recommendations are reciprocal, so travellers from the same countries are permitted to travel to Denmark, provided they provide proof of a booked six-day stay.