The "math class" approach you describe is for babies. It is the students' job to do this on their own, or have the TAs cover it in section.
With these approaches you cannot cover as much material. It is style over substance. But if you are going slowly and not trying to cover much material, I suppose it can't hurt.
Ignoring* the phrasing, the point here is one that I've heard many times - that somehow you do your students a disservice if you actually take the time to teach them the material. I believe the root of the disagreement is based in whether or not you believe that your job is to teach the material, or just present as much as possible. While I certainly don't believe it's my job to make the students to try to learn (in other words, if they don't do the homework there's only so much you can do), I do believe it's my job to actually teach the material. Yes, this involves doing examples in class. Ideally, I think it also involves doing your best to keep your students from falling asleep in your class, however early in the morning it might be. I think students learn best by interacting during class (plus it keeps them awake). And it's not just me that thinks this (see Freire, Dewey, Piaget, or generally constructivism).
I'm trying to teach in this style during the Algorithms summer term class I'm currently in the middle of. Unfortunately, I'm partially falling victim to the second argument - "but if you take the time to teach, you won't cover as much." Even though I fundamentally disagree with it (assuming that you want the students to actually learn the material, taking the time to teach it is never wasted), I can't figure out a good way to teach the vast number of algorithms that I think I'd be doing a disservice if I didn't teach, and still spend long enough on each one so that they really understand the underlying details. (This is made especially hard since the class meets every day, so there's no time for contemplation between classes.) I'm doing examples in class, having discussions about the algorithms, having them try sample instances, etc. Yet my idealist nature is somewhat unsatisfied.
On the other hand, I've assigned a half-term long programming project that does embody these values and which I'm very excited about. More on that later.
*Actually, I can't quite bring myself to ignore it altogether. While I'm glad not to be seeing a Barbie-style "math is hard," the idea that anything having to do with math class is "for babies" is rather absurd. Some things that are for babies; diapers, bottles, toys, mushed carrots. Things that are not for babies; Calculus, Algorithms, going to college, taking my classes.