Running the world is quite troublesome, and usually, motivated by qualities like greediness, jealousy, &c. Those qualities are very first ones to avoid as you start getting into mindfulness state. Hence even with superpowers (especially with those) yogis should more likely stay away from running the world, just by nature of the things.

Perhaps the overlap between people who meditate and sociopaths is low.

Why would yogis want to run the world?

I don't think the parent said he wanted yogis to run the world.

I believe he said that if yogis could really project their thoughts, it would be a super-power which would enable them to run the world.

The conclusion is that since they do not run the world, they likely do not possess such super-powers.

I do not believe that one can achieve supernatural powers with meditation either (for I have not seen someone with those).

Assuming they have such superpowers, they also need the desire to run the world. Hence, this way of concluding that they do not possess such powers does not seem right.

I like this mental exercise.

I agree that it is possible that they have the mental projection superpower and no desire to run the world. That would make sense, at least from my cursory knowledge of yogis :).

However, their philosophy has a central tenet of minimizing suffering. Wouldn't they use their superpower to eliminate suffering to any extent possible?

And a counter-point to that is, what if they do have the superpower, and they do use it, and that is why there is less suffering in the world than there otherwise would be.

It looks like what we need is a double-blind study.