A lot of functionality is only available via signals. For instance, there's no way other than SIGCHLD to be asynchronously notified when a process exits (unless you want to dedicate a thread to running wait()). There's no way other than SIGWINCH to be notified when your terminal gets resized.
You could certainly imagine some kernel extensions that take all of this useful functionality and make it available in ways other than signals, leaving just signals for things you have to deal with immediately like SIGSEGV (so you can print a nice error message before quitting), but they don't exist yet. I imagine some of the intent behind signalfd was to do this all at once for all signals, but it didn't quite work.
You could certainly imagine some kernel extensions that take all of this useful functionality and make it available in ways other than signals, leaving just signals for things you have to deal with immediately like SIGSEGV (so you can print a nice error message before quitting), but they don't exist yet. I imagine some of the intent behind signalfd was to do this all at once for all signals, but it didn't quite work.