I haven't seen the OSX Help menu but I've seen this feature implemented in several other program on Windows and Linux years ago. They don't seem to catch on but I'm not sure why. Maybe it's habit or the fact search seems like more effort or the need to know the exact name for something or that people prefer the 'presence' that menus give to options. Personally I think it's great, as long as there's an option to restore menus so you can 'browse' like you suggest.
What’s great about OS X’s approach is that it’s always there, in every app. (Some apps disable it which is a good way to make me angry.) Especially when you open up a brand new app or one you are not using frequently it can be frustrating to get your bearings. I can, for example, never remember where I can lock or group objects (I’m not even sure whether those commands are usually in a consistent place), the search is a good way to find out whether that functionality is available and where I can find it, also for future reference. Scanning menus for a specific command when I have no idea where it is is very frustrating for me.
This wouldn’t really work if every app had to implement this feature on its own, probably in different places and with slightly different behavior. Even if the behavior were consistent you still could never be sure whether you can search in the first place, that uncertainty is in my experience a good way to make sure a feature will never get used.
The OS X Help menu combines the two approaches. You type the command name, and it opens and highlights the appropriate menu for the result — complete with a big animated arrow next to the item you're choosing — so then you know where to find the menu item next time.