First off, it will never happen that all countries all over the world will recognized and regulate Bitcoin. That is already dreaming a very impossible dream. Tell that to China, Russia, India and the likes and we will b getting a good laugh. I am not saying there is no possibility that the minds of the leaders of these countries will not be changing but suffice to say that for now and in the near future that is not going to happen. However, let's assume that all will, I don't think fiat has to stop working. In Japan, Bitcoin is recognized and regualted but we still see yen very much alive. I don't understand why do we have to make Bitcoin a killer of other currencies when in fact here in the world of cryptocurrencies Bitcoin has so many competitors and they are doing just fine (well, except for shitcoins!). Can we not dream of making Bitcoin and other existing currencies co-exist peacefully with each other?
There is really no point in making Bitcoin the "salvador del mundo" or savior of the world's economy. I don't think Bitcoin is designed for that, in the first place. This is like putting a very heavy expectation and obligation on the part of Bitcoin and then years from now we will just be frustrated and disappointed why Bitcoin has not been the messiah we are looking for.
Obviously, if there will only be one global currency left which is Bitcoin then all values will be the same. Whether Bitcoin can become like a commodity or not, it does not matter at all. In my opinion, Bitcoin can be acting like a currency (medium of doing business) or a commodity (like gold, store of value) depending on how a person is using it and both can be perfectly fine with me...the only big problem is if a person has no Bitcoin at all then he failed to participate in the greatest revolution in human's financial/banking history happening right before our own faces and fingertips.