Sort of. I've done a lot of thinking about this one, and realize that it's really not just "one person" but a very large team of individuals, along with the "politics" of everything. If the President brings on a good staff, makes solid cabinet appointments, and they themself being a singular large part of the legislative process in modern years--given that it's usually fairly difficult to get 2/3rds of Congress to agree on anything--you can see the President actually has significantly more influence than you'd think.

In addition, it's the circles that person runs in and the circles that person's people run in. Do you think judge or cabinet appointments are decided on by one person? Sure, the President is a figurehead in this position and ultimately has to say yes or no, but there's a large pool of candidates out there and it's up to the staffers, maybe friends, maybe people in the know to propose those people to the President.

So while on paper the President doesn't, or shouldn't have that much power--in actuality with our current political process it's certainly much more.

Now, that said, just like the billionaires--they can only control so much. At least in the United States, there are competing interests even among the wealthy class, and sometimes shit just sort of happens--like a meteor killing the dinosaurs....or the release of decades of e-mails, videos, documents, and communications surrounding their pedophile behavior on a secret island in the Caribbean.