Hebrews 10:8 means exactly what it says. The plain reading is clear. And, it has widespread support throughout scripture.
PSALM 51: 16 For thou hast no delight in sacrifice. If I were I to give a burnt offering, thou wouldst not be pleased.
ISAIAH 1:11 ”What to me is the multitude of your sacrifices? says the Lord;
I have had enough of burnt offerings of ram and the fat of fed beasts; I do not delight in the blood of bulls, or of lambs, or of he-goats
The difficulty comes because the sacrificial ‘system’ is a foundation for some foundational, traditional doctrine. And, as well, they are pivotal for the rituals of atonement.(example Yom Kippur).
The sacrifices that are in question are specifically the Sacrifices for ‘sin’ - we know this, or rather this is made clear in David’s response to his great ‘sin’, when he didn’t make any sacrifice to atone, but repented.
There were many sacrifices, and the other ones, example thanksgiving, first fruits, were not, and are not in question here in Hebrews 10. It is only the ‘sin’ sacrifices.
Theologians have apologetic arguments explaining these verses, or sometimes explaining them ‘away’. This answer is not interested in participating in this discussion, as you only asked “What did God not desire” - and that is clear, very clear, … sacrifices, specifically ‘sin’ sacrifices.