"It seems in most environments as though you see students for at most 2 hours/week (except the intensive classes or the camps). That seems incredibly short, but you imply it happens in the public schools as well. How common is that? do most environments give ESL teachers many classes and very minimal hrs/class?"
It depends where you work. At a hagwon you'll see the students more (2-6 hours/week). Some people choose to work at hagwons because of this. You really will get to know your students on an individual level and see significant improvement in their English ability.
Public school and uni? 1-3 hours/week seems to be the norm. And yes, it's far too little for much long-lasting benefit to occur. And you really won't see improvement in most of your students, or even get to know them individually. It's frustrating to me a lot of the time. In Korea, people don't seem so concerned with actually learning English, as opposed to the appearance of learning it. And the appearance of learning it consists of having a foreigner, preferably a white North American at the front of the class for even as little as one hour/week.