Reminds me of the early Windows shell replacement days (LiteStep anyone?) and people had trouble understanding that Explorer.exe was both file manager and desktop shell. I don't think it's anything restrictive going on, just a deal where it is impractical to separate caja the desktop with the icons and caja the file manager. In Windows one of the things people did during ye olde Windows 98\SE\Me days was patch the three desktop shell files to be able to retain the functionality they needed.
I seem to recall a recent kerfuffle with Solus Budgie because they finally decided to patch out their increasingly old Nautilus which was still providing desktop icons in order to maintain compatibility with Gnome. Their drop in replacement left something to be desired... I imagine this is a similar situation. Caja provides the desktop. It's going to be difficult to try to run something else and keep Caja from wanting to do its thing.
With all the other stuff Wimpy has to do to keep us compatible with GTK3 without breaking the whole Mate Desktop it simply might not be a priority to make it possible to split the functions to allow a different file manager to run and then have to keep maintaining that against changes from a hostile upstream?