Google have a similar requirement already, try registering for a new Gmail account without providing a telephone number. They will allow you to register but then after a period between a few minutes and a few hours you will get a message saying "Google has detected some unusual activity on your account and needs you to provide further verification" and you won't be able to login until you verify it using a mobile phone number.
Sure you can in the UK still get pre-paid sim cards without providing ID to remain anonymous but how long before they close that backdoor to.