Ankle sprains and subsequent ankle vulnerabilty seem common in tennis. Although there are some excellent ankle braces out there, I'd imagine that a high shoe in addition to an effective brace is better than just a brace alone. So why is it so hard to find shoes that cover the ankle? Most of the big athletic shoe manufacturers don't even make a mid, let alone a 3/4 height tennis shoe, but they all make high top basketball shoes that incorporate a strap and other means to stabilize the ankle. What's the deal with this?
Seems to be at least partly a function of trend/fashion. There were quite a few mid shoes for tennis from the mid-80's till the early to mid 90's. Some say that Agassi wearing them had a lot to do with it. If you've looked carefully at the basketball market, the same has happened to some extent. While pretty much all of the top of the line basketball shoes at that same time were full high tops, and almost no players at the college and pro level wore anything else, the typical basketball shoe now is quite a bit lower, almost a mid top by comparison. Also, there are now quite a few low top basketball shoes, which there hadn't been since the 60's or earlier. This recent increase in lower top shoes may also be due somewhat to an increased premium placed on mobility in both sports.
In addition to the trend factor, there were a number of sports medicine research studies done in the 80's and 90's, which showed that high top shoes had surprisingly little effect on protecting ankles from sprains and tears. The only real benefit found from high and mid shoes was that it provided a tactile "reminder" to keep the ankle in a straight position, which in some ways helped avoid landing on a slightly turned or non-level ankle by accident. However, it was found that in the event of an inversion (a roll where the ankle goes outward and the foot goes inward under the body) or eversion (the opposite, where the foot splays outward), the support of the shoe itself was almost irrelevant to the severity of the outcome. Even a fairly solid high top apparently wasn't enough of a support to protect the joint. A real orthopedic ankle brace or air cast (or a good taping from a licensed trainer) does a better job and I think they figured that if you had any of those, adding a higher shoe wouldn't be adding any additional usable safety. Also, some of those support methods are fairly bulky, and mid and high top shoes can sometimes make it hard to get them inside the shoe.
N.B. Personally, I like the feel of a mid top shoe, and miss the ones they used to have. I recently got a pair of the mid top version that came out of the Barricade 2 and love them.