consider the influence Ayn Rand had

Let's see... Soviet Russia lived (relatively) happily until 1991 when it imploded through no effort of Ayn Rand. Libertarianism is not a major political force in any country that I know of. So, not that much influence.

What could stop them?

Oh dear, there is such a long list. A gun, for example. Men in uniform who are accustomed to following orders. Public indifference (a Kardashian lost 10 lbs through her special diet!).

some would quickly be rich or famous, be able to contact anyone important, run presidential campaigns, run think tanks, dominate any areas of intellectual discourse they care to, etc

Are you familiar with the term "magical thinking"? Popper couldn't do it. Ayn Rand couldn't do it. DD can't do it. You can't do it. So why would suddenly you have this thousand of god-emperors who can do anything they want to, purely through the force of reasoning?

Trump only won because his campaign was run, to a partial extent, by lesser philosophers

I think our evaluations of the latest presidential elections... differ.

a good philosopher can go into whatever scientific field he wants and identify and fix massive errors currently being made due to the wrong methods of thinking

You are a good philosopher, yes? Would you like to demonstrate this with some scientific field?

Even a mediocre philosopher like Aubrey de Grey managed to do something like that.

de Grey runs a medical think tank that so far has failed at its goal. In which way did he "fix massive errors"?

Have you read Atlas Shrugged? It's a book in which a philosophy teacher and his 3 star students change the world.

... (you do understand that this is fiction?)

try to imagine someone with ~100x better ideas and how much more effective that would be

We're back to magical thinking (I can imagine a lot of things, but presumably we are talking about reality), but even then, what will that someone do against a few grams of lead at high velocity?

He spread bad ideas

Did he believe they were bad ideas? How is his belief in his ideas different from your belief in your ideas?

a few people survive childhood

Since my childhood was sufficiently ordinary, I presume that I did not survive. Oops, you're talking to a zombie...