Of late we could see Phone Verification method is used in account registration forms so as to prove one is not a robot (e.g., Google signup form). So how popular is it's adoption rate? And how much it has increased the user's confidence to submit their own number.
Phone verification should not be used to prove that you are not a robot, but to prove that you are you, and to ensure that would be hackers need more than just a user name / password to get in.
Phone verification just to prove that I am not a robot would be a huge deterrent for me to even register at a site. As it would for sites that hold information me that I do not consider "sensitive".
Also note that that the two-step verification process for Google accounts is an optional extra security measure.