I guess I represent the opposite end of the spectrum, compared to the dojos described by Paula. I actually started in a university group (lots of beginners, and lots of large groups of people at the same kyu/level), and the dojo that this group evolved into maintained a high proportion of beginners.
So, for a looong time, every time koshis were practiced, we didn't throw. Nage just loads, and uke just "gets ready" for the fall--ie we are shown what ukemi should be like, as you are laying across the hip. Shown how to not be limp, shown where you will be reaching for this throw (be it under the arm, lapel, etc), shown how to pay attention to being ABOUT to fall.
So then everybody's comfort level goes way up over time, and since nobody is ever pressured by the instructor to finish the throw, people just start throwing when both partners are ready.
So over the course of a few months and 3 or 4 or so practice sessions, I was getting thrown.
A certain amount of the ukemi I think can be learned safely in a "load only no throw" environment. To get yourself so prepared actually makes going over soooooo easy.