Adding a couple of thoughts to this post on the subject.
Blood was not simply prohibited. In Leviticus, when Israel was in the camp, every sanctuary animal that was slaughtered, even for a normal meal, had its blood put on the altar. In Deuteronomy, when Moses readies Israel for a situation when the sanctuary will be more distant, he commands them to pour out the blood on the ground. The promised Land is more sanctified than the wilderness and it functions as a secondary altar allowing a secondary Levitical status to all Israel.
One reason for the prohibition then, is that the blood was given to reconcile us to God and then to give us life. But there is no point in the OT economy when the reconciliation is completed. To start drinking blood would be to claim that God’s wrath had been satisfied with the blood of bulls and goats. But it never was. Only when Christ died was that propitiation made. Now we can ritually drink his blood. (Nevertheless, the prohibition on blood remains in force and Leithart gives some reasons why.)
Reading and hearing Leviticus lately, I’m struck by the command to sprinkle blood seven times before the curtain to the Holy of Holies. Was the priest to keep trying in the hope that something would happen, only to give up after the seventh attempt. Jesus bled much farther away from the Sanctuary, yet even at t a distance the sanctuary responded by tearing the curtain in two.