I'ts better to just have the passport as back up. I'ts a last resort type of deal. If america was ever bad enough to leave in the first place, renouncing citizenship in the U.S. would be ur next step. So, worrying about 2 sets of taxes wouldn't really be on the plate.
You're correct. The way it works, for me at least, is...i leave america on my U.S. passport and when i arrive in Chile i check in as a chilean citizen using my Chilean passport. At that point i can then travel freely to many different countries not as a U.S. citizen, but as a chilean.