I just bought my Catalina 30 in October and it has a different kind of davits that I had never seen before. The "davits" are mounted on the pushpit rails and have a curved part that you hook the tube on one side of the dinghy onto. This supports the weight of the dinghy and then you secure it with the painter and maybe another line. See picture.
Two obvious drawbacks to this are that it blocks the swim ladder, but you would probably drop the dinghy in the water at anchor anyway. It also blocks the stern light, so you couldn't have the dinghy there if sailing at night.
I suspect that I will mainly use the davits as a place to store the dinghy when I'm not using the boat.