This is part of what I am finding so intriguing about jettisoning Greek/Roman thought. Thank you for the Hebrew perspective.
I cannot believe there is any efficacy ANYMORE (at least) in the blood of animals. Atonement... covering, was done perfectly in the blood of Yeshua, and for all time (perhaps to the beginning thereof).
However, there are many types of sacrifice which are not about atonement - Praise offerings, First Fruits, and etc... I don't know exactly how all that works out.
But I DO know that the prophets show those sacrifices being resumed... and at least 3 Holy Days that transcend His coming - I am content with that, as by that time, we will have THE most marvelous Rabbi to teach us in truth.
I wonder though, if your point does not apply more broadly, too: Many things might be better understood from the Hebrew perspective.