Phone based web server

I was talking to a friend and he had a brilliant idea. It is something like how users can host their own website or blog in their personal computers for free using certain software in their PC. Why not the same be implemented for mobile phone. Many mobile phones have huge storage capacity and bandwidth. If a software be developed by which mobile users can host their own websites easily by just installing the software then it would save so much bandwidth of hosting the same website in the host servers. One just needs to keep the app open for it to work. If a huge amount of people start hosting their own websites on the app then it would save a lot of bandwidth for the host servers.