it's an interesting question ... but it's not practical.
First of all, let me cover the 2 examples you gave as part of your "mobility" concerns:
Planes: they use addressing from ISPs via satellite and your communication wouldn't really be that much different than WiFi access from one coffee shop to the next. Your WAN IP might not change as often as you might think because of the satellite's range to the plane in motion. Even if it did change, there really isn't too much that you would need (as a host) to update (as a consumer). Let's give the totally unrealistic idea that you were hosting a website from a plane.. then I would give a totally unrealistic answer that you could use a dyndns service. Or, if your website were THAT important (perhaps government) then perhaps you should consider getting your own static IP for that webserver in the sky.... all the time.
Cars: As a cell user passes from one cell area to another, the base station from the cell provider is passed using a tracking system and is based on your cell strength, position and projected path. Because the ID of the phone being used stays the same, the base station always knows which cell ID is using which broad spectrum of frequencies to make a phone call or be directed to a WAN anyway. So, it's kind of (in a way) already being used that way. Anyway, I would really like to hear of a more practical situation where the cell would ABSOLUTELY NEED to have the same exact address all of the time to remain on a network. 3g doesn't work that way, so again, it's not practical. I'm only using 3g as an example because of phones and because of wireless cards that use cell tower networks. A satellite link to a laptop could be thought of in the same way as the above example... just a "slower moving" plane
The internet is based on routing... plain and simple...
routing DOES NOT forward a MAC address, plain and simple...
You are basically arguing the idea (your professor is) that would be impractical and impossible to change. But... for the sake of being a student, let's answer the question in the best way we can....
So, your MAC address is tied to your network card. EVERY network card in the world has a different address right? So, If I replaced my network card... that means that this address would have to be known throughout the world, in order for the world to communicate back to me right? Call it DNS or call it the "DNS alternative" it doesn't matter what we call it, it's still a fact that we would have to propagate this new address the quickest way possible EVERY TIME a network card is changed??? hehehe, I don't think so.
In the long run, it's MORE overhead on every network built around the world. Call it DNS or something else... doesn't matter. Even if MAC addresses were passed, you are talking about multiplying the number of traffic-based collisions by at least 10 fold. This is why IP and especially IPv6 exist, to broaden out communication possibilities given the number of nodes that we have out there... not simplify it. By limiting the traffic out on the public internet based on "changes" we are making it a little more complex, sure... but more efficient.
This is all hypothetical of course... one thing needs to be said before all of this though. MAC address communication over a convoluted WAN, such as the Internet, would mean changing EVERY routing device and changing EVERY router out there. You would be changing the pure definition of networking as we know it today. You would have to start with a fresh device and .. then sell it. But, with alternatives available... it's not practical.