Why is that? A solid axle is much cheaper to manufacturer and, when setup correctly (the Mustang has a damn good setup with a 3 link and panhard bar) they will outperform an independent setup at the dragstrip (where probably 80-90% of Mustangs are raced) and can achieve virtually the same level of performance around a road course, with the stipulation that larger bumps can upset the rear balance mid corner.
People tend to scapegoat the solid rear axle because they don't understand what the real problem is. The real problem with the Mustang is that its too softly sprung, the bushings are too mushy, and the sway bars are not stiff enough from the factory to support real hardcore cornering. Doing that though could compromise not only the regular day-to-day comfort, but also the straight line performance unless lots of money is involved, and the Mustang has always been about its low price.
So you can buy a Mustang GT, order a set of polyurethane bushings, new lower control arms (better geometry) stiffer springs/shocks and some thicker anti-roll bars (can all be had in handling packages from Company's like Griggs) and you have a very competent-handling car. There have been many, many race cars and good road cars with solid Axles (Jaguar D type and E type? anyone?)