registering to an account by an sms link in a mobile

It is well known that when using email for registration, one puts a registration link inside the email. It is also known, that when using a phone number (SMS) for registration, one uses a registration code (e.g. 4 digits) and needs to enter it into the screen of the mobile.

We would like to use a confirmation link in the SMS, in the same manner, it is done by email but for some reason its less of a standard. Am I missing something here? is it bad practice to put a confirmation link inside an SMS. Assume the link will be short (so it can fit the 140 characters limit)