I agree with Michael that koshinage is not necessarily a basic technique, wherever aikido is practiced.
Me, I have some "second thoughts" about it. It is pretty much a kokyunage with an obstacle (tori's hip), so why not skip the obstacle?
We still do some koshinage at my dojo, from time to time. Not much, but just so that the students get a bit familiar with it, since it is practiced in many other aikido dojos, seminars, and so on.
To get a really good ukemi for koshinage, it has to be practiced almost as much as is done in judo - and most aikido dojos would think that there is just not enough time for that, with everything else to learn in aikido.
A very prominent aikido shihan once told me that tobikoshi, hard fall, is for the young. When you get up in age, you should avoid doing it too much (or at all).