In the earlier civs the total production of a city was a big factor in its pollution chance. That is all gone, replaced by the health factor. I still find myself worrying about that, then I remember that it doesn't matter how much production you actually have. If you are working mines then your population isn't going to be maxed out, so your health problems should not be too severe.
I also used to wait and not build coal plants, but since I found out that the health demerits go away if another power source replaces I build them now. And I have found that I can either come up with enough health anyway or that the health problems that I have just keep me from working those last two coast squares.