People routinely run their own servers. A great example is bittorrent where the incentive design forces people to run actual file servers on their computer.
People will run servers on their computer if it is (i) motivated the right way, (ii) as frictionless as possible.
For the types of applications that web2 is great at (content creation / consumption), it makes no sense to run a server of course but computing is a lot bigger than that.