Extra vertical space? Fullscreen to me means no bars whatsoever. With bars, it's merely maximised at best. I consider it false what happens by F11 in Evince.
There's something to that I suppose, although I have to say that having some controls at hand can be quite useful. Actually I would argue that in a decent window manager (i.e., pretty much anything but Windows

) the answer's obvious: what you call fake full screen is already available in Xfce under Alt+F11, whereas the F11 implemented by the app in question could go for real full screen. Or maybe real full screen should be under something like Ctrl+F11.
Only if your interface is English. I wouldn't consider Alt+F a standard convention when even F11 isn't. [...] Luckily it says so in the menus.
In Dutch I would expect it to be Alt+B, not Alt+F. The specific key is besides the point, which is that I expect those icons to respond to the same keys they always have since the 1980s if not earlier. In English, "File options" (hamburger) is Alt+F, "View options" (document with wrench) is Alt+V, and so on. In Evince you can't even press left and right to switch between the button menus! The (acceptable!) cop-out I first encountered in some Microsoft programs, but later also in Firefox, is that the actual menu is still there and it just pops out when you press the relevant keyboard binding like Alt+F, Alt+T, etc. Because frankly Alt+T, D is a lot easier to remember than Ctrl+Shift+Y.
Opera/Blink responds to Alt+F, but it feels slightly less elegant in that it only responds to that (nor does it properly underline the access keys). So you have to press Alt+F, v, d for developer tools, which may or may not be easier than Ctrl+Shift+i depending on where your hands are.
Now admittedly this isn't
universal in the sense that Apple does something different, but this is universal on MS-DOS (at least in Microsoft programs), Windows, old GNOME, KDE, Xfce, etc.
Your last sentence is also of particular interest. In the menu-wielding Evince in Xubuntu,
keyboard bindings are indicated in the menus. The vanilla Evince in Debian does no such thing. This explains why I didn't know about Ctrl+N earlier. It does have a little keyboard shortcut help dialog available (also in menu-Evince, either under the help menu or with Ctrl+F1) but you don't come across those organically. Incidentally, Ctrl+F1 is not mentioned in the keyboard shortcut window. This means that in vanilla Evince, this binding is a complete secret.
I like the way I can navigate menus in Elinks for example. Esc to bring up the menubar and the rest can be done by arrow keys. Esc or Tab, whatever else it does in the interface, should land on menubar too and arrow keys should open and navigate the menus, as a standard convention.
While it would be rather annoying to do something like that (because is Esc better than Alt+F or just different?), it would be a more interesting thing to try than breaking all keyboard menu accessibility in the name of touch.
Once you're pro with the keybinds for most actions you need to do, Alt+F should be unnecessary.
Except they are keybindings for all intents and purposes. Sure, the most frequently used actions tend to have slightly faster or more convenient alternatives, but for something with a lot of menu options like Word or Writer the menu
is the keybinding. You don't press Alt+whatever, obstinately look at the menu, and press the next key. Arrow keys or the mouse would likely have a very similar result. No, what you do is you press the keyboard combination of Alt+s, m. Like this:
https://vimeo.com/200643905 You could create your own keybindings where the defaults are lacking. But I try to avoid going down my old Opera road.