Same reason they don't all wear hightops.
which is? (an honest question since i dont know the reason.)
A few research studies have shown that the likelihood of a sprained ankle is not increased when wearing low top shoes playing basketball. I'm pretty sure most athletes just do it for the comfort.
However, I have yet to play basketball in shoes below the ankle.
Edit: here's one of the studies: http://www.ncbi.nlm.nih.gov/pubmed/8368420 just so you all don't think I pulled the info out of my backside
From my experience, it all depends on the shoe itself rather than purely "high top vs low top".
I do honestly feel that
as a general rule high tops do give more support and reduce the risk of rolling an ankle. I say this mainly because I've never (in my entire life) rolled an ankle while wearing high-tops (or even mid-tops) but I have had a few minor rolls while wearing low tops.
However, there are exception in both cases. For example the Kobe 8 / Kobe 8 Elite is one of the lower cut shoes out there, but despite being one of my most played-in shoes I have never rolled an ankle in them. The way the shoe is designed and cut it gives excellent ankle support and stability despite the fact that it's low cut. The same is true for the CP3.VII, another low cut shoe that I have found to be extremely stable and supportive.
On the other hand the CP3.VI AE was a shoe that I had worn only 5-10 times because every second or third time I played in that shoe, I would end up with a minor ankle sprain at some point in the game. I'm not sure what exactly it is about the shoe, but it got to the point where I was too cautious about injury, and so I would play slower and less aggressively every time I wore that shoe.
When it comes to mid or high tops I've had no problems. Lebron 11, AJXX8 SE, Melo M10, AJ XX3, Rose 3.0, Penny V, Superfly 2, etc. I've played many aggressive hours in each of these shoes, and never even come close to rolling an ankle.