Honestly we could, or there could be something that could be developed to do this. But in my opinion a network admin won't setup a network this way, at least I wouldn't. There are reasons why we have static IP's, the ability to create a network of IP's that we designate, and that IP changes from place to place, security is one huge reason.
I guess I don't understand the question in that why would you want to setup a network like this. I mean the question it says IP's are a problem, but to whom? Not the network admin, not the user, the only problem is for someone who is trying to hack the network and would love to know the IP's used within that network. Say you worked at AT&T and you had a network in the midwest of say 50,000 computers and devices. Lets pretend that network was comprimised and you need to create a new IP network. Right now that is as simple as a few button clicks, but in a MAC address only world you would have to go through and change out 50,000 NIC.
Maybe i'm not getting it but I just don't see the benefit of only using MAC addresses as a network identifier.