I used not to pay much attention to the details of pronunciation although I know a bunch of phonetics concepts. As long as I could get myself understood, I was ok with it. Since I started with NCE reading, I have found lots of problems I missed or ignored before, like EE or AE pronunciation. I also found my ears become sharper and more sensitive than before when I listen to the news or other English programs.
In the NCE studying, you have book CDs to follow with. You can also put your own recording on the forum to let other learners to pick errors. Because of its popularity, it has lots of followers. People can study from each other and help each other, which is not what one can achieve in daily conversion or self-study. To be frank, no native speaker will stop to correct your pronunciation during the daily conversation; at most they will just pardon you if they can’t even guess out what you are trying to say.
The way you have suggested is also a very good way of learning spoken English. I just don’t agree you have such a negative opinion on NCE studying unless you have been through the whole set seriously and felt it is a just failure to you.
Anyway, I think we need do intensive English reading besides extensive reading. Of course, you can pick whatever textbooks you like. Don't have to stuck with NCE. Quote a Chinese Saying here - "Details determine success or failure"
Just my 2 cents