Generalized shapes might help if you're drawing extremely regular objects (books, balls, apartment buildings) or perhaps if you need to draw a generic "horse" from memory but it's not a big help with life drawing. Edwards and other life drawing teachers often suggest drawing the negative spaces as a way of breaking the habit of using the brain to figure out what the object is "like" (e.g. it's like a square sitting on a circle) and focus on what it is.
I think of them both as techniques for the same purpose - to get you to draw what you see as there rather than what you know is there. (Or even drawing the symbol for what you know is there.)
It's been a while since I've done any drawing, but from what I remember you can easily use both in the same image - blocking out the constituent shapes with approximations with around the right proportions, and then making sure that the negative space looks about right in the gaps in between.
Yes, negative space is useful for focusing a student's attention on the shape itself rather than the subject. But it also has the tendency to encourage a local rather than global focus, so that locally all the shapes look right, but the global proportions are wrong. Or where you work your way around a bicycle wheel drawing all the negative shapes, and the last shape you draw is too wide or too thin.
Which isn't much of a problem for things like still lifes, but it becomes a bigger problem in, for example, portraiture, where the human eye is particularly sensitive to errors in proportion -- which is why Edwards includes some construction rules-of-thumb in her portraiture chapter.
You may be focusing too strongly on "circles and squares" as idealized shapes... If you look at the picture of the elephant in the article, none of the shapes is quite a circle. Rather, they outline masses, like the blobs you might see if you defocus your eyes. Being able to capture the proportions and locations of these masses is actually very important when drawing from life. (see, for example, Nicolaides's "The Natural Way to Draw")
