I never really got into the exotic steels, as close as it came was ATS-34 and 440C. That said, I don't think I am far off when I say that one other tradeoff is how keen an edge you can get. With properly heat treated carbon steels and properly heat treated stainless steels, it just isn't possible to get the stainless as sharp as the carbon.
For most uses, say hunting, this doesn't really matter. But you won't make a straight razor out of 440C and expect it to be as fine an edge as with 1084 or 1095. Because shaving hair from your arm and shaving stubble from your face are two very different degrees of sharp.
I have recently gotten into spoon carving and the tools I use leave the final surface on the spoons. This means that the sharper the knife, the nicer the spoon. I finish them pretty fine. And resharpening isn't really a thing with carving knives. When they start to lose their bite, I strop and keep them sharp. They should never get dull at all.
As said, I am ignorant about the really exotic steels, so only take this as one man's experience with a relatively narrow range of steels. But there are good reasons why leaf springs, saw blades, carving knives, and files are made from fairly simple carbon steels. You use the best steel for the intended purpose. If your primary purpose is corrosion resistance, use stainless (I'd hate to use a carbon steel fillet knife for salt water fishing), but if your purpose puts more value on resilience, sharpness, or toughness, you will have to find a way to maintain the surface and deal with rust.
-Patrick