It wouldn't make sense for bitcoin to kill fiat currency since it is entirely backed by fiat currency.
Face it, if you couldn't exchange bitcoins for dollars, not one single person would bother with them. Just go to any thread where someone is scamming/selling something. Everything is translated in US dollar value.
It is more accurate to say that fiat is backed by Bitcoin than to say Bitcoin is backed by fiat. Money, in whatever form, is only as good as what it can be traded for, and it makes more sense to hold Bitcoin than fiat since one suffers from indefinite inflation and the other doesn't. Realistically, neither of them are backed by anything tangible. If America woke up tomorrow knowing what fractional reserve banking is, you'd likely see a financial revolution, and people would stop caring about USD, and instead care about trading resources and units of value that don't suffer from inflation.