Vertical integration is the solution, not this drilling cargo cult.
By vertical integration, do you mean that ExxonMobil should only refine the oil it pumps from wells it owns? Or that Valero needs to buy some wells?
Since the oil companies own only about 7% of the oil supply, and most of the rest is owned by sovereign governments who are in the market for selling wells, the only way for your vertical integration effort to work is to either
1. let Venezuela or Saudi Arabia buy ExxonMobil and Valero so they can vertically integrate.
2. Or, let Valero & ExxonMobil start drilling ....
The only thing vertical integration would change in this political environment is that politicians would have only one place to apply price controls that would ripple down to the well head. Of course, all that will do is shut down the wells as the owners wait for a better political climate and a better price.