The problem with this otherwise good idea is that google will not allow you to keep this account as an island.
Eventually you will get the "we've noticed something suspicious about your account" dialog which requires entering some other, unrelated phone number. You're locked out until you do so.
The suspicious behavior is, of course, signing up without a live phone number.
Ironically, they will accept any number you input with no verification that it is related to the account in any way. They just want to see a live, carrier number input.
(This has been my experience from within the US)
This is not true in general. It probably at least depends on the country you try to sign-up from probably other factors.
I think you can use Google Voice number on everything other than your main Gmail account.
So, to be extra safe, after you've set up your 2FA for gmail, make sure to change your recovery phone # to something other than your main telco or google voice number.
This is how 2FA was meant to work. It should always require a physical device only you have access to. Otherwise it's just using 1FA two times.
Too bad they really dumbed down the interface - it's not possible to delete messages from the new site.
1. Do NOT secure your sensitive accounts (facebook, primary email, bank accounts, twitter, etc) with your telco phone #. Telco Phone number is NOT secure!
"Create a brand new Gmail email account. Do not connect it to any of your existing email accounts. (When signing up for a new Gmail, you don’t need to enter a phone number or current email, although there are fields for you to do so. Leave them blank.) Once you’ve created the new island-unto-itself email address, create a new Google Voice number." Use this Google Voice # to secure your primary accounts, and don't have your telco # listed in any of those accounts.
But, make sure your New Gmail account is super secure, with a security key, as mentioned in the article.
2. Check the password recovery methods for all your sensitive accounts and make sure the answers aren't duplicated from any other site. Actually, it's best to remove them, if you can.
If any security experts want to chime in, please do.