What people have generally suggested is to start with a normal lens. On a full-frame 35mm camera, that role was generally filled by the 50mm lens. On a modern crop-frame DSLR, it would be closer to 30mm (for Canon APS-C 1.6x sensors) or 35mm (Nikon, Pentax, Sony) or 25mm (Olympus and Panasonic).

The 50mm is usually suggested these days as the first good supplement to the kit lens. It doesn't really matter whose 50mm lens you're looking at, the design for the f/1.8 (or f/1.7) version has been around forever. They're all sharp to very sharp, lightweight and (most of all) cheap. And as you pointed out, they'll function well as a shortish version of the traditional medium telephoto portrait lens. But as nice as the "nifty fifty" is, it's not a normal lens on a crop-sensor camera.

A normal prime lens is very versatile. You can step back a couple of feet and get a fairly wide image field. Step forward and you can fill the frame with a single subject of interest. Neither picture will be quite what you'd get using a wide angle lens or a short telephoto, but you can get a reasonably good picture either way. The field of view subjectively matches what you tend to think you're seeing in real life, so there are no major surprises or unintentional special effects.

Working with a prime lens, though, helps you to become a better photographer. It forces you to change your point of view to find the best image rather than just standing in the easiest spot and turning a ring. You might get acceptable results using a zoom exclusively, but it's unlikely you'll get a spectacular result until you've forced yourself to take the rocky road for a while. You may decide to stick with primes (I have always had zooms, and shot an average of ten rolls of film a day -- or the equivalent -- for a couple of decades, and I bet I took fewer than two hundred shots with a zoom lens in all that time) but even if you use a zoom lens most of the time, you'll never use it in quite the same way after working exclusively with prime lenses long enough to change your habits.