Makes absolutely no sense to me that anyone would want fiat to be integrated into the bitcoin system. Not only is that pretty much impossible to do (since how are you going to integrate a centralized currency into a decentralized one?), it is also bad for bitcoin, as it would mean that it has ties with fiat and isn't an independently decentralized currency anymore.
Have you not heard about USD and bitcoin pairing or any fiat currency pairing being listed in exchanges, you really do not need to do anything else to pair these currencies together and it is not bad for bitcoin as people usually invest in bitcoin with their fiat currencies as they do not have the power to create wealth from vacuum.
These are the two main reasons why people still use bitcoin, instead of fiat. The most unattractive trait of fiat currency is that it goes down in value over time. Bitcoin is a hedge against that, so even though fiats are still readily available to be used, some people will simply diversify their wealth into bitcoin. There is nothing wrong with that whatsoever.
If you look at the stats only a small percentage is using bitcoin, the strength of a fiat currency depends upon the financial structure of a country and if they have a solid infrastructure and good economic policies it will not depreciate in value over time, people like to diversify their wealth in every investment platform and we are yet to see institutional investments coming into this market and when that happens the price would rally to more than a trillion dollar valuation.