VISA is related to identify of a person. You can’t just ignore this and completely exchange it with Bitcoins.
Currently as I have heard you can easily travel through Bitcoins. You need to buy gift cards of popular booking sites through Bitcoins and use those to book tickets to travel through the world.
So yes half of your dream is fulfilled in one or another way.
Moreover regarding the VISA thing. It won’t be changed I guess, as it is top priority for a nation’s security.