Also a US President who is antithetical to the oil/lng industry will drive up the price of oil through the futures market. Demand is still high, Biden has constrained supply, forcing futures prices to go up. Trump was bullish on oil/lng, with the same demand and increased supply, prices went down.
Seems to me if they wanted to increase production a lot they would decrease the stock buy backs and instead increase future revenue by increasing current and near future production.
Additionally, there's the push to expand LNG exports to Europe.
Both of these are major factors in the price rise. I personally don't really care about this as I don't own a car, and this will push new buyers towards EVs, but the media silence on this is kind of instructive - corporate media is owned by the same investors profiting off the high energy prices, so there's no incentive for honest reporting, not if you want to keep your media job anyway.
America no longer supports the House of Saud. It tolerates it. But were it to face a serious threat, apart from a Wahhabi fundamentalist, the U.S. would be unlikely to intervene. Riyadh knows this, which is why those calls aren’t very useful.
That said, the President does have dials. They are drilling permits and import restrictions.
I'll focus just on the first half: Less than 10% of oil drilling happens on Federal land, and there are thousands of unused permits available.
Which isn't to say that these thousands of permits could be drilled on tomorrow - they are subject to environmental impact studies, lawsuits from locals for dozens of reasons, supply chain issues around equipment, etc.
Which is a long way of saying: This particular dial is very indirect, at best.