the user is not going to intuit that the function
must be invisible because he can't see it
User intuition changes over time as familiarity with new interfaces is gained. A system whereby edit/action buttons appear only when the mouse is on the right hand side of the screen seems reasonable -- if users have trained themselves to expect this behaviour and UIs consistently use this pattern in predictable ways.
If every user interface with mouse input used a "hover the cursor to the right of the screen for edit/action buttons" pattern, it'd become quite natural to users.
Gnome 3 is a good example of where hidden elements are used successfully. Hovering the mouse in the top left "Activities" corner of the screen will show hidden content. The bottom right corner of the screen also shows hidden content (this time, without any visual affordance). Users learn to expect the hidden items to appear when hovering the cursor. No affordance is required. The downside is that users may not be able to discover this behaviour without help from a tutorial or manual (at least until "hot corners" become a standard UI pattern).
Those are specific positions on a screen in a desktop OS UI. That's HUGELY different from yet-another-webapp, because you only need to learn it ONCE, and then it remains the same always, no matter what app you're using or what page you're viewing.
With web pages and apps, it's up to each designer to decide where and how things are laid out, and everyone has their own opinion, so if 20 designers decide to hide their components, how is the user to find them? The last thing I want to do is play hide-and-seek moving the mouse around a webpage/app randomly in the forlorn hope that maybe one of the gadgets or magic locations will pop up a control that I can use.
Put in a gear icon that I can mouse over. Put SOMETHING there that says "hey! I can be interacted with!" Otherwise I'll just ascribe the interface as designed by someone incompetent and look for an alternative.
What you describe works fine in theory; the problem is that in practice it's ridiculously easy to overestimate how likely the average user is to train themselves to expect this behavior. In general, we (power users, developers, etc.) tend to adapt to consistent UI behaviours very quickly and to overestimate how difficult it is for an average user, but when it comes to things that are _invisible_ until you do something, the gap is much greater yet.
If every user interface with mouse input used a "hover the cursor to the right of the screen for edit/action buttons" pattern, it'd become quite natural to users.
Gnome 3 is a good example of where hidden elements are used successfully. Hovering the mouse in the top left "Activities" corner of the screen will show hidden content. The bottom right corner of the screen also shows hidden content (this time, without any visual affordance). Users learn to expect the hidden items to appear when hovering the cursor. No affordance is required. The downside is that users may not be able to discover this behaviour without help from a tutorial or manual (at least until "hot corners" become a standard UI pattern).