This article really should have been called "Security hole in Gandi's processes". Why would they change the account email address if you didn't reply to a single email within 24 hours? Who thought that was a good solution?
"Gandi’s paper 'email reset' form makes a lot of sense in the world where most of their customers are individuals or small businesses with one or two domains, and using addresses that they may lose access to. With no other factors, if they lose access to the email address and forget their password, there needs to be a process to regain access."
If a customer loses access to the one e-mail registered with GANDI (a small business signs up with their Earthlink.net address, moves, and now only has a Comcast.com address), there needs to be a way that allows an e-mail change without requiring positive confirmation from the old address. Having GANDI change process to disallow this when an account is 2FA-enabled is, to me, a reasonable compromise.
The alternative would be to go to a fastmail selected notary, and present appropriate identification material to them, and then pay a small fee to have an expedited (3 day) recovery process.
In Germany you can do that with the German mail system - the postman will then check your id and confirm you are who you claim to be. Certainly not foolproof, but just accepting incoming letters at face value seems crazy.
In here postmen only check your ID when receiving or retrieving packages, but I've understood that you can buy the same service for letters as well. Most online identity checks are made by logging in trough banks, which can verify your SSN and alike.
You don't have a bad idea, you just need to consider all the effects.
For the places where it's really necessary, like fastmail, they should have physical photos of all the principals on hand.
It's expensive, but it's also an extremely precious resource they need to guard at all times.