To be fair: oil being fungible means that it doesn't much matter who gets Iraqi production or the direct profits from it. So long as that oil can be produced and sold by a regime not under international sanctions, it will increase market supply thus lowering price and giving the market a little more wiggle room to absorb supply shocks.

Which are goals much more in-line with American defense strategy in the region as a whole.

So while the view of our having invaded Iraq to steal their oil remains naive, it's hard to argue that the US receives no benefits from that oil being produced by a non-sanctioned (non-Saddam) regime.