Durga,
The Internet would break 
Seriously, it would, and here’s why: Let’s say we tried to use MAC addresses as a layer 3 identity for communicating between devices at a distance (not on the same local network). MAC addresses are burned into the network cards by the manufacturer, and each card has a unique MAC (in theory). The problem comes when you are trying to keep track of who is where. The reason that the Internet is able to function now is primary due to a protocol called BGP that figures out the best way to get from one IP address to another.
Even though there are millions and millions of connected devices, BGP is able to function by using groups of addresses–most BGP providers will reject routes for any network smaller than a /24. Being able to group large numbers of IP addresses together and treat them the same is critical so the memory and processing power required to run BGP wouldn’t overwhelm a router’s resources. In the case of try to track individual addresses on a per machine level (like we are thinking about doing with MAC addresses), this would force BGP to deal with the equivalent of /32 routes. Since devices can easily move from one location to another, there just isn’t a way to “lump” groups of them together. There would just be too many objects to keep track of within BGP!