Some applications, like digital eyes, which connect directly to the optic nerve, would be first used to cure blindness, but soon people would start replacing their functioning eyes too, if it allows feeding pixels directly into the brain. Same with prosthetics, if they'd be better than biological ones. Then if you have cyborg eyes, arms and legs, why have a biological 'core' which is pretty much useless at this point.

Storing the brain in the body would actually be a bad idea. Human brains could be stored in a warehouse and they'd control robotic bodies remotely. You'd be able to jump into different bodies all over the world, and choose from different form-factors (ant, whale, dragon, etc.) This would actually be easier to implement, because the life-support system for the brain could be larger and consume more energy and other resources. You'd also be able to choose whether you want to live in a simulated world or a physical world through robots.

I think this is where we're quite realistically heading in less than 50 years.