It is said that bitcoin will destroy the fiat system but i believe that if this happens the world will change completly because banks and a lot of things will go out of market.
The destruction of the fiat system by Bitcoin is possible but very unlikely. Banking is an established thing in this world since around 2000 BC and I don't think anything could destroy it in the near future. But in the long perspective, in 200 years maybe, it is quite possible IMO.
Our world is ruled by the government. No matter which country that is, the government is totally in control. Democracy is just a term that they use, it's not even real anymore. Anyway, fiat money is just one of the ways the government controls their people. They will definitely put up a fight just to make sure that Bitcoin doesn't take over.
But, there's no way they could battle Bitcoin because it's just a data. That would be their major problem in making sure that fiat stays since Bitcoin isn't being controlled by anyone, then they can't blackmail, threaten, or have an agreement with somebody about Bitcoins.