" How do you handle kicks since they seem to be very widely used outside of Aikido...."
Aikido techniques can be applied against kicks easily enough. The main reason most Aikido clubs don't practice kicks is because it's so easy for uke to get injured. It'svery difficult to fall when somebody has entered under your leg and you're falling vertically head first from a height. Even if your hamstring doesn't tear you're in a sticky situation.
And like any other attack, you can enter around it. Unless you're slow.
There's an mpg of Christian Tissier with a kicking uke at the aikidofaq, although it's sped up.