The president appoints multiple people on the board of the fed. But that’s about it. More to your point neither the fed or the president has any control left on the main causes of inflation. Principal of which is corporate greed. Every major market in the US is an unnatural monopoly due to the fact we stopped busting monopoly’s. Corporate greed would not be an inflationary cause but since there is so little competition in markets they can conspire without communication. Neither the president or the fed have any levers in which to do anything about this realistically since half our legislation is wholly owned by those same companies that hold control over these markets.

Companies very literally trained judges through continued learning requirements to not fight monopolies. The only bar for a merger today is a single question “Will prices go down” companies lie saying “yes” then it gets approved and there is no recourse or follow up.

They further make fallacious claims like “Monopolies don’t exist without government!” Which is a total farce perpetuated by the same groups. It’s meant to have people vote against their interests. Monopolies are an inevitable consequence of capitalism. It must divide at a certain point or stagnate.