Some people are working on this problem. You might be interested in looking at the Matrix standard [0] or some of the things built using it like Riot [1], a Slack-like web client supporting text, voice and video communication for one-on-one or group contexts.
Thanks for your feedback! I agree, WhatsApp is an amazing piece of software with a great user interface & UX.
There are significant computer science challenges when building peer-to-peer software that are much easier to solve when building a centralized system. This may be the reason that people seem to "brag" when they create something p2p - because it is difficult to do - and it may also be the reason why there has not been in your opinion "a killer p2p chat app" yet.
One great thing about WebTorrent is that it makes building p2p software for the web much easier. They have done a great job!
Matrix is a great project! I believe it uses a federated model which means that it relies on people donating their servers and bandwidth and messages pass through those federated servers rather than directly between peers as with WebRTC.
We need to build our own p2p and e2e secure chat client like whatsapp which works on every platform.
Sure, it's possible - skype was exactly this before except for the e2e part.
Why we techies can't? Let's make a group and dissect the problem in our free time. Who is up for it?