And if 99% of the population is too dumb to do it, then it probably doesn't need to be done.
This is very hard to believe. That's basically conceding that we will never cure cancer/colonize mars/solve productive nuclear fusion etc.
The country with the highest percentage of PhDs is Slovenia, at 3.8% of 25-64 year-olds.
I know academic performance doesn't perfectly equate to IQ, especially at this level because right now smart people have many other options, but on the other hand that's the highest percentage and the OECD average is just short of 1.1%.
OECD PhD percentages: https://doi.org/10.1787/888933978645
China I'm not sure about, but seems to be about 500k/year, so if I estimate population of 1.5e9 and 80 year life expectancy, that's a steady-state level of 3.75% of the entire population.
So the minimum for those things being above IQ 125 seems at least plausible. May not be correct, but it is plausible.
As for "why should they get significant power?" — well, 'should' is a question of values. Do you believe in democracy and self-determination? Or is it fine to treat them all like animals, by which I mean spay, neuter, euthanise without asking their opinions, and/or selectively breed to be decorative and fit into handbags? Because the worst horrors that Charlie Stross and Ian Banks and Harlan Ellison have imagined are all as easy as Fully Automated Luxury Space Communism if you have an AI which can automate almost everything, regardless of whether anything remains purely in the domain of a tiny elite.
I'm going to support democracy. That's why I think an unemployable 99% should have, in a reasonable sense, 99% of the power.
As for why the 1% may have much more than 1% of the power in practice… that's kinda where I was going with the Hyper-Dystopia vs. Fully Automated Luxury Space Communism example: whoever controls the AI gets to play as Gods to a much larger degree than mere billionaires get to act like real life is a Civilization/KSP/SimCity game, and the default for who controls the AI is whoever has skills such that they can't be replaced with an AI. Or the current rich, if everyone can be displaced by AI.
It's not specifically what was written, but it's what I see between the lines.