Well SHA256 is a red herring here: one could suggest any suitable fast hash, non-crytopgraphic hash instead.
Yes, it takes time linear in the length of the thing you are sorting, but comparison sort is generally worse in that respect: comparison also takes up to linear time in the comprands, and you have to compare each element not just once but log n times [1].
So the time to hash all the elements once (if the hash is not already cached in the element) is going to be a small part of the sort time.
[1] There are ways around repeatedly re-comparing the entire key, but they work mostly in specialized cases.
Yes, it takes time linear in the length of the thing you are sorting, but comparison sort is generally worse in that respect: comparison also takes up to linear time in the comprands, and you have to compare each element not just once but log n times [1].
So the time to hash all the elements once (if the hash is not already cached in the element) is going to be a small part of the sort time.
[1] There are ways around repeatedly re-comparing the entire key, but they work mostly in specialized cases.