Right, but Deuteronomy is okay with the spilling of the blood of cattle and other sacrificial animals apart from the sanctuary. So Deuteronomy is simply allowing the eating of the meat of nominally sacrificial animals without it constituting a sacrifice, just as eating deer is allowed without it being a sacrifice.
It's been about twenty years since I've thought about this issue, so I suppose I could use a refresher course. My impression was/is that Leviticus does not
allow the secular eating of sacrificial animals (unlike Deuteronomy). IIRC, it doesn't address the issue, at least. This is why, in my view, there were so many "high places" and altars and temples up to the establishment of Deuteronomy. And why was there never a Passover celebration in Jerusalem until Josiah? As 2 Kings 23:22-23 puts it:
Neither in the days of the judges who led Israel nor in the days of the kings of Israel and the kings of Judah had any such Passover been observed. But in the eighteenth year of King Josiah, this Passover was celebrated to the Lord in Jerusalem.
did people celebrate Passover between the days of the judges and Josiah's time? Presumably at the various high places and the Shiloh and Elephantine temples. Even figures in the Deuteronomistic writings (despite all the talk about sacrificing in one place) sacrifice with God's approval outside of wherever it was at the time God "chose to put his name."
1 Sam. 7:7-9:
When the Philistines heard that Israel had assembled at Mizpah, the rulers of the Philistines came up to attack them. When the Israelites heard of it, they were afraid because of the Philistines. They said to Samuel, “Do not stop crying out to the Lord our God for us, that he may rescue us from the hand of the Philistines.” Then Samuel took a suckling lamb and sacrificed it as a whole burnt offering to the Lord. He cried out to the Lord on Israel’s behalf, and the Lord answered him.
1 Sam. 7:15-17:
Samuel continued as Israel’s leader all the days of his life. From year to year he went on a circuit from Bethel to Gilgal to Mizpah, judging Israel in all those places. But he always went back to Ramah, where his home was, and there he also held court for Israel. And he built an altar there to the Lord.
This was during the time Jeremiah says God had chosen to put his name in the Shiloh temple (in which Samuel had served). Deuteronomy retroactively "ruined" everything for everyone. Consider the law against kings having many wives. From my point of view this was a northern law aimed at southern kings like David and Solomon who had multiple wives. But from a "non-Deuteronomistic" perspective it was okay. But after Deuteronomy became established in Judah, it made these kings look bad (which was the original point, I'm thinking). Take the Damascus Document, for example, which excuses David for having many wives.
CD col. 5:
And concerning the prince it is written, He shall not multiply wives to himself (Deut. 17:17); but David had not read the sealed book of the Law which was in the ark (of the Covenant), for it was not opened in Israel from the death of Eleazar and Joshua, and the elders who worshipped Ashtoreth. It was hidden and (was not) revealed until the coming of Zadok.
Why were there so many high places (and altars and temples) before Josiah's time? Because, in my view, they were necessary because there was no such thing as secular slaughter of sacrificial animals (cattle, sheep and goats) prior to the establishment of Deuteronomy, and Deuteronomy, unlike Leviticus, had to grapple with the consequences of the centralization of sacrifices.
When the Lord your God has enlarged your territory as he promised you, and you crave meat and say, “I would like some meat,” then you may eat as much of it as you want. If the place where the Lord your God chooses to put his Name is too far away from you, you may slaughter animals from the herds and flocks the Lord has given you, as I have commanded you, and in your own towns you may eat as much of them as you want. Eat them as you would gazelle or deer. Both the ceremonially unclean and the clean may eat. But be sure you do not eat the blood, because the blood is the life, and you must not eat the life with the meat. You must not eat the blood; pour it out on the ground like water. Do not eat it, so that it may go well with you and your children after you, because you will be doing what is right in the eyes of the Lord.
From the perspective of Leviticus 17 (in my view), pouring the blood of these kinds of animals out onto the ground like that of gazelles and deer would be "bloodshed" and merit being cut off from Israel. But Leviticus did not have to deal with the ramifications of "if the place where the Lord your God chooses to put his name is too far away from you," since, as the OT itself indicates, there were many altars and high places to sacrifice animals.
Sometimes the songs that we hear are just songs of our own.