Travel to other countries without a visa? If so, how will the government recognize people from other countries and how do they know if he is clean from illegal activities?
But if you mean that we can pay using bitcoin rather than fiat/credit/debit/other payment, maybe we will see it in the future, which is our benefit because we already have bitcoin. But you can still dream like that and wait for when that happens but I guess it is hard to see yourself traveling to other countries without a visa. Maybe there will be another method to check every citizen from all countries.
I think there are countries right now which you can travel without the need of a passport or a visa but they are only limited and that is what the dream of the op all about, to extend those countries. I think it's possible in the future but If it's about the other visa (the card one) then it's pretty possible since many merchants now can accept different payment methods and this includes bitcoin.
We also have bitcoin cards and some of them have a support for visa. So if you see that visa sign, you can just use your bitcoin card on it. There is no need to bring your visa card with you all the times but bitcoin is already an all in one solution.