Thank you for this.
Phone numbers have little to do with two step authentication and everything to do with making the company's profiling of you more accurate so that they can sell you for more money. The only thing better that a phone number is your credit card details so that they get access to your financial history.
Two step authentication refers to things like the TAN numbers used by european banks or the RSA tokens/Soft tokens used in the the IT industry or good old one use pads used by spies of days gone by. (or the original printed TAN sheets).
Remember youtube is google so you are supplying them with yet another bit of info locking down your profile. Chances are they have it anyway but this way it is official and useable for every purpose they can think of to make money with your data in every country and not just n the US.