surprisingly coins from queen anne are not as rare as you would think, they come up for sale quite regularly on fleabay
Why? Many countries do not have mints of their own and instead contact with other mints, both public and private, to strike their coins. That includes both circulation and NCLT coins. The FM has made some very nice circulation coins for various countries, and they have made a lot of NCLT as well. So has the US mint, and Englands Royal Mint, and many other mints. If you like a coin buy it. If you don't want to directly support a country or government buy then on the aftermarket and hopefully at a lower price. But I can't see rejecting a coin simply because of what mint produced it.