Some about the treasures you can buy in internet

[Tarbicus]

But how do you control/police this?

I don't see how it can be policed. The police, quite frankly, need to be concentrating on murders, robberies, assaults of all natures, etc, etc. I guarantee this is low priotity for them, at a time when they are stretched to the limits.

One could, of course, register detectorists when they buy detectors - much like the case with guns. But is that really feasible?

It's not as serious as guns. Guns kill people, metal detectors don't.

I think the problem is that if the archaeology is to be protected, legislation would have to be as strict as possible... and things that would do no harm would have to be axed, too.

More legislation means even more criminalisation of the general population, at a time where (in the UK at least) little old ladies are being thrown into prison for what, ten years ago, was sensibly a non-criminal act and covered by non-penal fines. You will get NO sympathy from the introduction of yet more legislation, in particular from me for sure. "Make more laws" is the lazy answer to a problem, and does not necessarily take into account the reality of a situation or make any impact on it. It certainly overcrowds the prisons though, which in turn breeds more criminals, especially the way they are run now. Don't forget, there are already laws supposed to cover much of this.

Perhaps a database, where any detectorist had to state what and where they found things, and open them up to detailed analysis by a local authority before being allowed to keep/sell stuff - with the relevant body having first right to buy.

I think this is already in place here in the UK. There is certainly a means for all finds to be documented and provenanced, along with photos, and they are available even on the internet to view. I don't have the bookmark to hand, but will post it if I come across it. That's the right path as far as I'm concerned.