What's the point of DHCP then? Why do IPs exist if we're all flying around on the internet with our MACs?
I'm not suggesting we're anonymous, I'm just suggesting that our hardware IDs aren't flying around online like you suggest. I run a bunch of websites with Google Analytics and Webalyzer, no hardware IDs.
I've run Wireshark, Fiddler, no MACs.
You get IPs, IPs go back to router, router's DHCP has local IP assigned to MAC.