More than "reinventing the web", I would worry about finding strategies to keep the web open against the strong pull towards (semi) walled gardens that is coming from Facebook and others.
People do care about privacy and openness, not just in the way technologists expect them to. Using Google for mail over some random company or running your own mail server is reasonable for the threats against privacy most people face. Communicating with your friends on Facebook is "open" compared to asking them to buy a specific phone, run their own servers or install software. If anything it's developers don't care about privacy and openness. They are the ones running all these companies that take advantage of open technology not (or even prevent it to) keeping up with the demands of users.
How? In this new economy, big corporations have structured themselves such that they can compete with and protect against "disruptive" startups.
Also, coming up with something more attractive takes time (trial and error), and big corporations can easily incorporate (copy) those new features in their products in the meantime.
The network effect is just too strong, and most people don't care enough about privacy and openness to switch to different networks.