This seems like a good idea until you realize that you are the only one using a random mac address. (There is a vendor prefix at the beginning of every mac) Better would be to take a bit more care in choosing a more realistic address.
I would advise to use a VPN connection. In this case it doesn't matter that you've randomized your mac address in a way which can be clearly identified as random. And even then you can see the VPN server IP in the logs so you should also make precautions and buy your VPN connection anonymously (and even then - you'll never know if you're really anonymous).
Changing your mac address seems to be sufficient (in addition to the VPN usage) to prevent easy tracking through something unique like your real mac address. But I agree that this is just 1-3 lines of code for realistic mac address generation so it should be unproblematic to add.
Edit: If you have fears of being uncovered by random-looking mac addresses without vendor prefixes, changing your mac address will probably not help you. Your threat model is different - maybe APT-level - and you have to do way more than changing your mac address.
Takes 5 minutes to configure your OpenWRT router to log all DNS requests: https://superuser.com/questions/632898/how-to-log-all-dns-re... Or if you are an attacker without control over that router: search for dns spoofing. I did this several times to demonstrate companies that their public networks can be hijacked.
Unless avoiding this becomes common practice and then the whole story changes.
> Unless avoiding this becomes common practice and then the whole story changes
If that means that everyone starts to use random mac addresses, you still can't identify specific persons based on their randomized mac addresses when they change them every time they reconnect.
As @_fink on Twitter pointed out, colliding with a real existing MAC address is not ideal.