We may be missing the obvious because it is neglected in dogma and creeds. Law's ability to convict and cut to the heart concerns how it interacts with sinful behavior - it affects a potential sinner or a person after sinning to think an innocent (even cuddly) animal like a lamb will die because of sin. This is its power. The deterrent and convicter of innocent pure sacrifice. The pageant too of noses being rubbed in sin by rituals like children today being told Father Christmas only gives nice gifts if they have been good - yet in the Law it is in truth not invented stories. Now roll forward and a greater innocent life is shed for the acts that make it necessary - this convicts the guilty doesn't it. Genuine love for Jesus and His loving Father adds to that conviction and cutting to the heart more than a dying lamb. Now this conviction is so great to the one living God and His Son that ritual on top of the sacrifice is unnecessary. Truth about it does enough convicting. Now the convicting added to by a Spirit of truth coming from God and applying that truth to convict too all has so mcg power that sin can be wiped iut and slavery to it broken as chains fall off. But one ritual remains to remind and reconvict - the bread and wine - the command to partake in rememberance of Him.
