The blog post cites visible damage from door delivery shipping as the major design issue that they were trying to solve.
(Paper) cartons are much weaker and less resilient than plastic bottles. Think about the number of times you've seen dented or folded chicken soup cartons on supermarket shelves... I've certainly seen plenty of Safeway soup boxes to avoid because of obvious exterior damage.
I don't think cartons would get them very far in that area.
I've never really seen milk cartons delivered towards schools or shops (think juices and milk) be damaged all that often, but I'm not watching their deliveries either! I just imagined it was a problem already solved for non-pressurized drinks.
Then you're blessed with good fortune! Unfortunately I remember getting my lunch milk carton already sticky and wet from other damaged cartons in the elementary school cafeteria many times. Only the inside was waxed, so once one carton sprung a leak, the rest would weaken from the leakage, and sometimes when you'd go to pick yours up, it would tear and spill. Yuck.
The problem is the customer paying $4+ a serving won't find that acceptable. A school won't care if a few $0.50 cartons are dented in a shipping crate of over a hundred milk cartons, but a customer that gets a dented $5 drink is going to complain and ask for a refund/replacement.
(Paper) cartons are much weaker and less resilient than plastic bottles. Think about the number of times you've seen dented or folded chicken soup cartons on supermarket shelves... I've certainly seen plenty of Safeway soup boxes to avoid because of obvious exterior damage.
I don't think cartons would get them very far in that area.