It's true this is a mess, but no application should have a menu by icon as its only means of access. It's OK to offer that as an option, but all applications should be capable of presenting a user interface when launched from the Applications directory (or (rarely) ~/Applications, etc).

There's really no exception to this rule. For an (tiny) minority of applications, it makes sense to hide the dock icon, and to typically access the app via hotkey or menu bar widget. But those apps should still have an icon and should still be able to be invoked by opening it using any of the standard ways to do that. That's just how the Mac works.