Taking ipfs/ipns [1] as an example, having handlers inside web browsers would allow people to link from http[s]:// to ipfs:// and vice versa in a seamless way, lowering the barrier to migrate.
From there on, there's nothing preventing you from distributing your application code (html/css/javascript/whathaveyou) over ipfs, and make use of WebRTC for user-to-user interactions.
Obviously http[s] is going to stick around for a while as it has its use cases (basically anything that deals with a centralized service, from online banking to search engines to apis), but having a secondary, peer to peer means of distributing content and applications would be a major plus.
[1] http://ipfs.io (they have a working implementation in Go with an HTTP gateway as well as a FUSE filesystem)
So, how do we address this? Is there a "killer app" for the distributed web that will motivate people to move to it? Can we use existing web tech like Web-RTC to bootstrap the system? Maybe a workable avenue is mobile, where people are pretty comfortable installing new applications - what if we built the next social network into an app based on the distributed web?
I don't know the answer, but I'd love to hear any ideas/brainstorming you clever people have to offer.