I will keep saying this until I am blue in the face. Fiat and Bitcoin will not mix, the banks will never allow it because it will make them obsolete. What part of that do people not understand? Bitcoin was designed to replace the fiat system and here we have people trying to integrate the two, LOL. It will not happen!!!! Make no mistake, this will be an all out war between the banking system and Bitcoin.
I'm not sure what point you are trying to make -- are you saying that Bitcoin is some kind of play money that has no value when exchanged with fiat currency? Both have perceived value and as long as they do, there will always be exchange between the two. The world is not going to wake up to some libertarian-anarchist utopia and stop using government-issued fiat currency overnight.
Banks are hostile towards bitcoin, it's obvious, because it challenges their profits. They are providing resistance, which just causes people wanting to exchange between fiat and currency to find alternate methods that are more expensive, down to trading with moneypak joe. The free market predicts that there will be entrepreneurs that will build systems that are safer, cheaper and more more efficient than what currently exists for trading between the two. When banks see their profits from payment systems and wire transfers going down, they or their successors will start dealing in bitcoin.