Why is Kassadin not played in tournaments?
Solution 1:
He is actually very easily countered, as he specializes in countering standard mid mages, you just need to pick less common things to counter him, which does not happen as much in solo queue.
For instance, Fizz, Talon or any AD carry all counter him quite easily and make his laning phase quite miserable.
And if he gets behind, he needs to roam to get kills, and organized teams are a lot better at avoiding random jumps from him, due to warding, enhanced map awareness and better communication.
So essentially, it is too complicated to get ahead with him in a tournament and isn't worth the risk.
Solution 2:
The thing about kass is that he eats up mana, and is a snowball champ. That means is weak at first but then spirals into power, but the weak early game is a huge problem for him. If kass doesn't get any kills he doesn't do very well, but he tends to pick off champions by ulting through walls quickly.
He isn't played much in ranked because ranked games are all about how team works together. Annie, cass, ryze, malz, all have abilites that have cc, high damage, and aoe which works well with groups. Kass has a small AOE, which requires getting close.
TL:DR? Doesn't fit well in team fights compared to other ap because of high cool downs.