There is also that some services don't accept foreign numbers for authentication. Nor virtual phone numbers.
But it adds a layer of protection, doesn't it? Your known public phone number is one, your verification phone is another one from another carrier.
Is that really an additional layer of protection, or the same layer, slightly obscured? But probably not obscured from the attacker that managed to get your password and just needs the SMS verification code to get into your account.
The trouble with compartmentalizing with a separate phone is that the company with your money probably also sold your secret phone number (that they only required for security) so it will probably also show up on that whitepages site.
You have to give this phone number to a bunch of services that you use, i.e. all the ones that do sms confirmations. One data breach, and it isn't "secret" anymore.