If you tried to route everything with a MAC address, (which isn’t possible, but for arguments sake we will pretend it is) the problem is that when you take your phone with its MAC address off your wifi and on to your work wifi, Where would the registry be? How would the Internet know how to find your phone? Do you just log into one giant global registry so that everyone can find your phone when they are trying to communicate with it? That would be a giant fucking database and everyone would always be trying to use it.
This is a solved issue called EUI-64 IPv6 addressing. It is a privacy nightmare.