As part of rescinding a contract, you have to restore the other party to his original condition. You buy a car as a minor and want out, you have to give the car back, perhaps with payment for wear and tear and depreciation. You can't do that with a phone contract, and should expect that even if you manage to void the contract you'll remain responsible for the cost of the phone prior to the date you disaffirm.

Depending upon whether you are deemed to have acted within a reasonable time of reaching the age of majority, you may be able to avoid your contract going forward from the date you formally instruct the service provider that you're renouncing the contract. See, e.g., Almada v. Ruelas, 96 Ariz. 155, 393 P.2d 254 (1964) ("Where a minor has executed a conveyance and wishes to avoid its effect he must renounce the instrument 'within a reasonable time" after reaching his majority.'"); (St. Paul Fire & Marine Ins. Co. v. Muniz, 19 Ariz. App. 5, 504 P.2d 546 (1972) ("It is true that a contract entered into with a minor is voidable, however the contract is not disaffirmed until notice of disaffirmance is communicated to the other party.") I am skeptical that you can get any retroactive relief.