Seems as usage requires a $200 phone on a 2 year contract (or $500+ on an unlocked iPhone), plus an Apple ID, plus a credit card, plus network traffic will still be pushed through a single point it seems too expensive/traceable to be truly disposable and anonymous.
Can't Burner collect money from users for temporary numbers and then delete all records of number assignments when the numbers are "burned" by users? Twilio's recordkeeping might be more persistent though. Are there laws which effectively require Burner to maintain records? If not, Burner would keep a persistent record that User123 paid $2 for a number but could conveniently delete other identifying information.
Useful for avoiding telemarketers though.