No i dont think bitcoin will totally rule over the world .it will be totally different and its limitations will be more than 21 million .all the government will jointly accept and i am sure that it will not be bitcoins at all.
i think still it need a good time rule over the world. actually bitcoin is not yes so much popular in all over the world, it will take a long time when all the people of the world will starting using bitcoin and they will give priority to bitcoin over fiat currency.
But we cannot ignore people's capability on how quickly they will learn new things ?
You or your father is sending mails through postal like some 20 years back people were doing ? After mobile communication got introduced the importance of postal has gone.
I have already started giving priority to bitcoin over fiat. And I do see many people are doing similar things. So the possibility of having a next generation money has already started.