For me that actually ended up the only way to gain access back to an old account of mine. Luckily I was able to cooperate with the new owner of the number, and he was helpful enough to give me the code that was sent, otherwise I'd have lost a Google account with several hundred euros of purchases on it, despite having the password, control of the backup email, knowing all security questions, and knowing the exact date the account was registered (the only issue was that mobile carriers here re-issue phone numbers after 6 months without any calls, and I had put the SIM into a tablet).
The obvious issue with this is that the new owner of the number doesn't actually know if it's the owner of the old account trying to sign into it - it could be anyone trying to take over an account whos owner forgot to change the number for. And how do they know you're not trying to sign into their account? The text messages don't specify which account is being attempted or anything.
