The disadvantage of this is that there is no visual cue to the user that additional controls will appear.
Not every user will spend time hovering over your entire UI, searching for controls that you've hidden away.
This is a one-dimensional design decision. "UI looks cluttered, lets hide some stuff. Wow that looks better!". But from the viewpoint of a new user, you've just created a barrier.
Have you conducted any studies that show that? We have done this and so far no one has ever complained about "missing links/buttons". Most users never even noticed when we switched to hover controls
Have you done any studies to ensure that new visitors know that there are contols to discover? Perhaps they aren't complaining because they don't know they're missing stuff.
Could you provide more information about the experiment that you conducted? In real life, users have the option of quitting, and the luxury to do it in private; two things that are very hard to emulate in "experimental" conditions but which greatly affect the outcome. I'm not in any position to judge your experimental techniques, but if you're relying on users actively complaining about things, or worse, telling you what they think they want, you're probably doing it wrong.
It's my opinion that hiding menu items not a great idea for the reasons OP said. In my opinion, coming from someone who's had to use an interface which does this, is that it's borderline obnoxious expecting me to remember where, and that it's necessary, to hover over magical areas to show important controls.
I think having the items be very translucent until hovered provides the best of both worlds. I can see where they are, but are easily ignorable.
I think it's a little unfair to dismiss this design pattern just because it's not immediately discoverable on page load. It really depends on the context in which this is used. Also, while better looks is one thing, having less controls on the page leaves the user with a smaller cognitive load, giving them more attention to focus on and process the content.
Not every user will spend time hovering over your entire UI, searching for controls that you've hidden away.
This is a one-dimensional design decision. "UI looks cluttered, lets hide some stuff. Wow that looks better!". But from the viewpoint of a new user, you've just created a barrier.