I think we're partly talking past each other. I completely agree that most of the time, search is inconvenient for file access and the few times it is convenient, it's either because I or a a colleague messed up and something wasn't filed where it belonged or because I'm trying to make sense of a project I'm not familiar with. (And then I'm usually using find and/or grep, not the Unity file search.)
Where I find search to be superior to menus is in program startup and occasionally as a replacement for deep menu navigation. This is a very fast way to get to programs I don't use frequently enough to pin. So, windows key;c;a;enter and Calibre starts up. Windows key;g;enter and gjiten is there and so on.
Things that I do use frequently enough to pin are even faster. WIndows key + 7 and emacs is up. Still other stuff I fire up from a shell; xdg-open foo.pdf and so on. The whole system works well enough I don't need much pinned. (nautilus, firefox, write, calc, settings, shell, emacs, xpad -- and the write should actually be removed, I hardly ever fire that up from the bar.)
I agree that discoverability isn't as good as a classical menu system. I don't care, that's startup costs. I use computers intensively and startup costs are negligible compared to the total, so the relevant criterion to me is the speed I can eventually reach. And between fast application access and not having to drag windows around, I think Unity saves me an hour every week.
That's not for everybody of course. Somebody who spends their time in Gimp is going to be using the mouse far more often than I do. Even office software has many features that are easier with the mouse than the keyboard. So, no I'm not claiming this is a universal solution; I'm certainly not saying that everybody should switch. I am saying that it works for me and that works amazingly well for me.