Is it not the case that the prohibition on blood first appears here, and that this is because meat is first explicitly permitted here (Gen 9:4)?

This is, I believe, precisely correct. Again, while man might have begun eating meat just after the Fall, he was doing so without the explicit permission of God. God had not given his explicit permission in Gen 1 because the Fall had not yet happened; food from plants was at that time doubtless much more nutritious and tasty. But now, again, because the world is starting anew, and God is passing out the new rules of the game, only now does he acknowledge that eating meat is permitted. But if he is going to permit that, he had better (so goes the thinking) forbid the eating of blood, lest man think that is ever permitted. It is not, because (see above) the lifeblood is respected deeply as a symbol of the sacredness of life—of all life that draws breath. The importance of treating the blood as sacred is underlined more explicitly in Lev 17:10-14, which is well worth reviewing in full:

And whatsoever man there be of the house of Israel, or of the strangers that sojourn among you, that eateth any manner of blood; I will even set my face against that soul that eateth blood, and will cut him off from among his people. For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul. Therefore I said unto the children of Israel, No soul of you shall eat blood, neither shall any stranger that sojourneth among you eat blood. And whatsoever man there be of the children of Israel, or of the strangers that sojourn among you, which hunteth and catcheth any beast or fowl that may be eaten; he shall even pour out the blood thereof, and cover it with dust. For it is the life of all flesh; the blood of it is for the life thereof: therefore I said unto the children of Israel, Ye shall eat the blood of no manner of flesh: for the life of all flesh is the blood thereof: whosoever eateth it shall be cut off.