No. It will not do that.

The modern technical requirements of monetary mediums are far to diverse for one blockchain to be able to monopolise the entire world.

That doesn't mean that Bitcoin won't continue to dominate the marketcap - it may well do (see my post above). But it's already been left in the dust as far as technical performance goes. It is never going to be used as a day to day currency. (Gold wan't, even when its value backed all other currencies).