No, the primary reason is oil is a global market subject to global forces, and OPEC+ is the larger player in that. Their aim is to adjust production to match demand as well as they can to support prices, as well as they can. And they do a so so job of it.
If some "oil baron" could bump prices artificially, I'm sure they would, but they can't. If say Exxon decides to charge more for refined products, other companies may decide it's a change to take more market share.