There is ABSOLUTELY an option to enable 2FA on a Google account now that does not require giving them a phone number. There's a clear "Advanced Options" link that lets you choose a security key, which is what folks should be using anyway.
Other than security key, it's only phone number or adding account to the phone.
I'm sorry I didn't mention that in my post, I wasn't trying to lie, I just can't obtain physical key and I don't think I have to have physical key to read my emails.
Besides, you don't need an actual physical key for U2F.
If there is a way of doing it, I suspect it's deliberately well hidden. I also suspect what they enforce varies by country.