I've been scuba diving in Greece.
When was that?
It's not a dive-friendly country.
It could have been but that is changing fast.
They jealously guard their ancient artifacts
Yes the government is trying to do this (not very successfully) and I think they should given the importance, value, and amount of the treasures one can find down there.
are very suspicious of scuba divers.
Not if you dive with a local operator. I do dive mostly independently and everybody who sees us thinks that we are spearfishing (illegal with scuba here) - but that is their problem - not mine.
The water is typically pretty darn cold, the visibility is poor,
I don't know if we are talking here about the same Greece
Assuming we are talking about summer months (May to October) water is typically over 25oC. Yes at depth (>25m) it can reach 20ish but that's for a short time and in anyway I wouldn't call these "darn cold" . Winter months waters are usually around 18-23oC. Not darn cold either. Apart from temperature the waters are typical Mediterranean i.e. usually no strong currents, good to very good visibility, clear (no trash - no polution) but also with limited fish life - especially for big things. There are small things (nudies etc) but one needs to know what he is looking for.
locations for diving is limited because of the restrictions on diving
Depending of the place it can be - but no sane dive operator would open a business in a place that there aren't at least few decent dive sites. If you find a dive operator with good online reviews you can be sure that they offer at least some nice spots.
The Mediterranean in general is not known as a spectacular place for diving.
I agree - if you want spectacular diving go to SE Asia, or Galapagos or something.
Now my opinion. If you want to spend an exciting month or so JUST FOR diving don't come here - you will get disappointed. But if you want to have nice relaxing holidays with the kids playing on the beach etc and on top of this do few dives and/or snorkeling in very beginner friendly conditions to see nice underwater landscapes etc then Greece can be ideal.
I live in a very popular tourist destination - a city called Chania in the West part of the island of Crete. It is very family friendly area, with several (5 or so?) dive operators - some good - some not so. The place offers some very nice top side activities too (trekking/mountaineering, visiting ancient sites, relaxing on numerous fabulous beaches etc) .
Please ask more info if you are interested.
All the best