I know people use CrossOver with Steam on macOS, though that requires a rather intricate setup I don't know much about. I guess what you'd like to have is the kind of seamless integration that Proton has with Steam on Linux.
In practice Proton and CrossOver tends to have rather different sets of needs. Proton only supports Linux and is only focused on gaming. CrossOver exists for a handful of platforms, most notably macOS (which has a number of intricacies: missing 32 bit libraries, Apple Silicon, missing Vulkan drivers which requires MoltenVK, but MoltenVK itself cannot really offer all the features standard Vulkan drivers have on Linux), and is also used for non-gaming applications. CrossOver also lives in the form of specialized branches we develop for specific applications, on request of their developers. So while of course we share everything that can be shared, in my experience this tends to be not that much (except what goes upstream, of course). In pratice CrossOver and Proton live in different repositories, have independent build systems and independent release schedules.
note that I commonly buy all games that run on linux :)