Our classes run 1:25 each, and there are about 65 people per section. I'd say about 3-4 people are cold-called per class, and the 'duties' of the person called up vary with the class. For many classes, you could think of one person laying down the background and kicking off the case, another person or two addressing key building blocks or concepts along the way, and a final person who shows a model and gives a recommendation. So, the first person called on doesn't necessarily have the most challenging task, and how a class evolves depends a lot on where the students take it.
We also had a theory that contributing frequently would be a good guard against being cold-called, but I think most of us have concluded that this isn't the case. I volunteer quite a bit, and was cold-called in each of the 5 classes we had last quarter. In fact, one day I volunteered to say something, and the professor just continued with a tough cold-call. Someone in my learning team, who is in a different section and also talks a lot in class, wasn't cold-called a single time. I definitely get the sense that professors will call on people depending on which way the class is heading. If it seems like a lot of people are confused or if we're on the wrong track, they'll call on someone they are confident in to bring the class back in line. The opposite is also true; if someone seems to have the case nailed early in the period, they might purposefully try to get some other people involved to muddle the case up a little and bring in some additional ideas.
It can sometimes be tough to contribute when there are 65 eager beavers all in the same classroom, but you have to try because most classes base 25-40% of your grade on class contribution. It must be really tough with 90 people in the same room. Generally speaking, it's not left to a single person to walk the case through all the way, and we've never done anything like what GMATT described - at least not for class.