Well I see several problems with this interpretation here is some thoughts on it.
Firstly the bible does not show animal sacrifices in the millenium. That is something that gets assumed but that is not actually said. It gets assumed because is 66 speaks of sacrifices but the whole context is clear it is speaking about after the millenium.- Also because of the chapters in Ezekiel but that does not dictate the millenium either. It becomes assumed that Ezekiels temple must be in the millenium and the sacrifices must be literal but that is not the only possibility for those chapters.
Also why it is true that not all sacrifices were for sin, and so some could tecnically remain, the problem here is that God never desired sacrifice in the first place. And if other animal sacrifices were going to be needed after Christ came, then we would have commandment for them NOW.
If we do not have them now, then they can never be because salvation is only in the new covenant and that is an eternal covenant and a finished covenant in Jesus blood. There is no new covenant requirements for animal sacrifices.
However there IS sacrifices required in the new covenant. And they are all spiritual and they are all done by us in the SPirit. We are to both present out bodies as a living sacrifice- and we are to offer up the praise of our lips as an acceptable sacrifice which the OT calls the bullocks of our lips.
We should also keep in mind that we can prove that OT literal animal sacrifices were examples of spiritual sacrifices and truths.
To prove this firstly we see that Jesus is the fulfillment of the passover lamb. The original laws about passover in no way say that there will be a spiritual fulfillment of this but we know it is true.
We know that while Jesus was a lamb- so are we His lambs and we are to be led dumb to the slaughter just as He was and that He then provided and still provides that if we be sacrificed as he was, that we shall keep our life( the death angel passes over us) when we are told that if we lose our life for his sake we save our life. This is a spiritual sacrifice. It does not pay for sins as His did, but it kills the old man of sin our flesh.
these are just examples of many things that could be said for the real meaning if Ezekiel being prophetic of new covenant spiritual truth.
Just as the OT and laws were physical examples of new covenant spiritual truth.