Every place my club dove (admittedly probably the worst choices - my bad for not having my own car) charged. I think it's the places where the cruise tourists go. My experience on GC was extremely limited and didn't give me a fair impression. I so wish I had gone alone and had the option to dive the sites I researched. Unfortunatley the absolute proscription of solo even with the card prevents me from ever trying GC again.
I am sure that is true, because Eden Rock is a popular site with cruise ship divers and I know that they charge for weights.
There's been a lot of discussion about solo diving on Cayman on SB and the conclusion seems to be that most dive ops prefer to follow the guidelines (not regulations) against solo diving, probably because of concerns about liabilty - but not all of them.
Shore diving on Cayman Brac has been getting more attention lately. I have never tried it but you can ask
@vincent54 about it, and recently a member posted that the Brac Scuba Shack dive op are pleased to accommodate solo divers if they are certified and carry a secondary air supply, see the link below.
Shore diving on Cayman Brac?
I think that you might like Brac, it is absolutely NOT a touristy place and the cruise ships never go near it - and the diving is very good IMO, and you don't have to worry about someone breaking into your car while you are diving!
As I mentioned, we didn't really care that much for Cayman until our 3rd trip, that's when we discovered the Sister Islands of Brac and Little, and realized that there are also lovely places on GC away from George Town and the Seven Mile Beach. Before that we liked the diving and the convenience, but not the culture, but we have learned that there are more options and it has now become a good fit for us, especially at this time of our life.
The Caymans are expensive, no denying that, but there are ways to better manage the expenses and sometimes you get what you pay for IMO, so maybe you should take a look at Cayman Brac?