They've already clamped down on model rocketry as a hobby. I wouldn't be surprised to see restrictions on flying devices capable of carrying payloads larger than a certain size.
As you point out, it's not hard to imagine nefarious uses. Which is, of course, one of the reasons we can't have nice things.
The differences between model rocketry and model aircraft are significant enough that any "clamping down" on model aircraft would not be effective. The materials are too generic.
I disagree. You can pour your own sugar motor in nearly any impulse you desire. Granted technically it's not simple, but the materials required are easily obtained.
As for the rest of the rocket, I don't think the materials could get more generic. Fiberglass, carbon fiber, metal, and phenolic are all easily obtained.
They do have to leave their country to pursue their hobby. That may be some evidence of clamping. (they probably have to take to the water for safety reasons, but they seem to go amlot further outthan safety demands.)
They're still in Danish territorial waters when they launch. The reason they launch at sea is safety. It's hard to know exactly where the rocket will land, and there just aren't any good places in Denmark where there's a 50 mile radius where you can be certain that nobody will be hit by debris.
The part of the Baltic they launch from is actually a millitary training area that they borrow every year for launches.
Disclaimer: I'm involved with Copenhagen Suborbitals.
Considering there are multiple teams shooting for over 100k ft flights at Black Rock this year I'd say the US isn't as restrictive as they could be. For instance, here in Australia it's nearly impossible to get a waver for 100k ft flights due to the financial considerations.
As you point out, it's not hard to imagine nefarious uses. Which is, of course, one of the reasons we can't have nice things.