Well, I don't know, but I'd guess it has something to do with the chip's ability to switch voltages quickly. To send voltage to zero all you have to do is ground it, so a saw wave can be achieved this way. To achieve in a very quick rise in voltage (the beginning of a square wave) you'd have to have a really quick response.
I don't think that explains anything. I think it just clarifies the problem.
Basically, junky cheap stuff is junky cheap stuff, and there has to be some reason why a modular Moog still fetches ten grand.
After typing this I looked up some info on the TB303, which has a really rad square wave, and is (I think) FM. Its Wiki says this,
"The TB-303 has a single audio oscillator, which may be configured to produce either a sawtooth wave or a square wave. The square wave is in fact created by flipping every other cycle of the sawtooth wave upside down, giving it a specific, more hollow, sound a bit different from regular square waves."
Hm...