I believe and believe bitcoin will be able to compete and even defeat the traditional payment process that you said. we can see for yourself that there are currently more and more bitcoin hunters, it is not impossible that in the next few years bitcoin will master it.
That could happen if all countries decide to accept bitcoin and the other coins as the new payment system method so their people can make a transaction using cryptocurrency. So far, only a few countries which accepting bitcoin and another coin for another option of the transaction but soon, I believe that we will have more countries that will approve cryptocurrency. Cryptocurrency itself still grow until now, and we are seeing many new people who will adopt cryptocurrency, and they will use cryptocurrency in their daily life.
Countries will think twice to let people use cryptocurrencies instead of fiat (government can influence the fiat system, but just can't influence bitcoin system, which is not acceptable for the governments....)
What governments can do is to rule the exchange between crypto and fiat. There won't be a magic moment, when most of the people in the world will enlighten in a second and will know bitcoin and will turn to bitcoin. There will be a long period when people will learn about bitcoin, will try it and in the end they will get accustomed to it...
But while this period lasts, people just don't have the chance to use bitcoin everywhere, they will have to exchange some bitcoin to fiat, to pay bills, taxes, etc...
And this is where governments can influence bitcoin (not the system, but the acceptance, the adoption of bitcoin). If they make it hard to exchange bitcoin to fiat (KYC, searching for the origin of the bitcoins and maybe force people to pay tax when they exchange bitcoin to fiat), so if they want, the governments can slow down the adoption, because it's not their interest to let people choose something else then fiat...