A currency is just a debt title. Someone gets a service from you and "writes" you a debt title. then you take that and aquire something from someone else. BTC can replace that with some advantages - It´s decentralized and not inflationary. However it has to overcome it´s scalability problems. Moreover it should be more stable, price wise and fungible to become a real currency for everyday use.
I took bitcoin as an example but we can talk about cryptocurrency that will solve the problem of scalability.
So are there any problem theoretically speaking substituting dollars with a cryptocurrency?
There's no need to replace dollars for bitcoins and it would not be efficient in daily life. As a cryprocurrency it would do just fine, but as the dollar, although it's one of the most important, is not the only currency, you cannot just replace it for bitcoin.
In a near future all payments will be made via smarthphones or hardware connected to the net.
So what would be the difficulty in everyday use?
So what me and some people think bitcoin will be the global currency, it won't beat dollar and be more popular but it will be like a dollar, so we could just pay or do some things with dollar and bitcoin at the same time.
So what's the point to have double currrency?
Your example is flawed because not even the dollar represents the whole world economy there are many other currencies that are very strong, what I think it is going to happen is that bitcoin is going to become one of the strongest currencies of the world and a significant amount of trade is going to move through it, it is not going to become the first world currency because governments are never going to allow that.
So it will be another currency like other?
Again what is the point?
you are just exchanging your bitcoins for dollars just like you are exchanging your gold to dollars , there was no need to replace dollars with gold right ? bitcoin was just like that there was really no reason to make bitcoin replace dollar.
In this case i don't understand why we talk about "closing banks" "decentralized currency" if we can replace the paper money and the economy managed by bank etc etc.
In the long run ,without replacemenent ,who control the money will be on the top anywayright?