There is a big competition is going on between local currency and cryptocurrecies. If crypto enters in to the market surely it will disappear the local currency. Because the benefits is large when compared to local currency. So people automatically use cryptocurrency only. In future surely bitcoin will rule the crypto market.
Man, I do not see any competition between the cryptocurrencies and fiat. Local money will always exist as each country has many old people that will never understand crypto. Nothing to be afraid of.
It is too early to say anything like that and that I dont think so that any such thing will ever happen in near future. however, if there comes a situation when people are more inclined towards the crypto currencies, then the usage of the paper money will be reduced and that in that case, we may experience that people will then start investing more money into the crypto currencies instead of keeping the paper money into the banks.