The fact that people can change their MAC address means that that type of a user detection is not to much more accurate than an IP address.
Correct, but it can be one part of a more robust solution. The issue of two people in the same house wanting to play a game at once could be solved. For those paranoid against multikeyers, they could look at current connections and see if the MACs differ. If so, it's two computers, so probably good to assume two different people.
On top of that, if you directly gave the user's MAC address to the server, someone could potentially clone the user's MAC address and get them banned, despite having only logged into the wrong game.
The MAC Address could also be a factor in calculating if someone has been already banned. A MAC being the same definitely wouldn't be enough to warrant any sort of action, but an administrator could then look closer into the situation.
A MAC address is a not really a "essential liberty", but the right not to be named is. Assuming that everyone who doesn't want to be recognised is doing something wrong is a bad idea. Very similar to the freedom of speech, some people choose to abuse it, but it doesn't mean that others shouldn't have it.
The fact that people can change their MAC address means that that type of a user detection is not to much more accurate than an IP address. On top of that, if you directly gave the user's MAC address to the server, someone could potentially clone the user's MAC address and get them banned, despite having only logged into the wrong game.