It would seem that sacrifices were originally ordained by the Rabbinical authority, the same "Rabbinical authority ruled that prayer would take the place of physical sacrifices."
Manmade laws and customs, they change like light and shadows on a cloudy day. I'd say that "through observance of the Commandments, repentance and prayer" was and is orgininally the root of it all.
Abraham instructed young Issac to pick the best beast to sacrifice, to give up to God, thereby proving a willingness to experience loss to worship His Holy name. And, none of this had to be done in a temple, another of man's arbitrary customs. I'd say that "Commandments, repentance and prayer" to most folks is a greater sacrifice in their lives today that a lamb or sheep at that time. 