Maybe in the developed world country there will be less demand of paper money as they will go to full digital, the world is moving toward digital world if you have notice, we have a lot of inventions or developments to make our life fast and easy.
Hmm when you say developed I see Singapore. But I dont know man. Paper money got a lot of history in it. It will be hard for the government to change it specially for the people also.
But the government will have no choice if everybody is using bitcoin then what are they going to do ban the use of bitcoin if it's not regulated by authorities? That would make civil wars the next step lol anyways I don't think bitcoin will get far enough to be a real treat.