> There is  a commercial package called Maya. They have a pop-up
> window/menu widget they call "hot box". In that pop-up they have all, or
> as few as chosen by the user, menus collected in a transparent window
> they pop-up under the mouse after the spacebar is hold for a while (I
> think it was half a second).

`mouse3.el' does this.  But it's initiated by
a right-click, not by holding the space bar.

It could be made to also or instead be initiated
by a keyboard key.  But why?  If the location of
the popup is at the mouse pointer, why make users
involve _both_ the mouse and the keyboard?

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Why?  Because you could continue activating menus with keyboard so you don't need to switch to mouse. 

Why also a key even if mouse is active? Because holding spacebar with the thumb is very easy and can be done while moving mouse around,  but first reason is more interesting in my opinion. 

Also observe that I don't say it is better or faster. As you commented on the part below, I mean it mostly as something that makes Emacs more explorable for people that use starter kits with minimalistic guis where menubars are off etc.

Emacs aleady has all menus explorable from context menu, C-mouse2 opens global menu. "Hot  box" widget differs in how it renders menus, and adds some context sensitive zones, so it is some kind of explorable all-in-one options widget, or I don't know how to call it. Like a global context menu on steroids with prettier presentation then ordinary context menu.

> Maybe such or similar widget could be good to have in Emacs? As a
> compromise between a minimal GUI, discoverability and avialability of
> menus even when gui elements are disabled? A context menu would still be
> faster though.

See `mouse3.el'.  I think it provides what I
think you've described.
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I have checked it. It is not even remotely close,  not in a slightest :-).