My answers to the OP and the following discussion.
1) intelligence (if there is such a global thing, not wanting to derail into this debate here) is not directly correlated to social success. It might be at the margin, I have met a few bright individuals who ascended to success. But on average, good social circles, good family support, parents who value education and exemplify/explain good organisation and studying habits (external factors), or obedience and resistance to boredom and frustration (internal factors), seem more important than intelligence as classically understood to achieve a basic education or diploma good enough to allow the smarts ones the headstart needed to success, and the not-so-smart a comfortable life.
2+3) So yes, here we have an "intelligence privilege", or rather, see my first point, an "educational and life opportunities privilege" (that, in a lot of cases, can simply be boiled down to a class privilege, even more so in countries where education costs money).
As people with this privilege will tend to gravitate towards the control of societies, it's their responsibility to ensure the protection of the less-privileged.
Actually, it should be their interest, either via empathy (helped by the off chance one of them or their kids loses the privilege), or simply, on cold calculation, because the security cost (monetary or freedom restriction or worse) of keeping the underprivileged violence at bay will end being worse than the cost of protection.
Of course, as we have seen that this privilege doesn't necessarily mean actual intelligence, the lack of empathy, the "it'll never happen to me or my kin", or the lack of understanding of the full cost analysis, seem prevalent in our world...
4) yes, your garbage man or cleaning crew can be quite intelligent, or have skills you don't have.
Their problem is that their skills are much more common or much easier to train by the employers than scientific or medical skills. So their employers can use market forces to pay them less.
But I can't fault their employers for that. Making money and competing against similar companies is the goal that our society assigns to companies, they're simply playing by our rules. And as all societies who've tried to completely do away with those basic market rules have failed so far, and I don't want my kids killed in a violent revolution, I won't advocate suddenly killing all those rules. I feel like us human still need a "reward by greater ownership of nice things" system.
So, I agree with point 4, it's up to society to protect the underpriviledged, via rules (limited ownership of common/indispensable goods, environment protection, labour rules, minimum wages) and redistribution (taxes, supports, citizen revenue if you're as a leftist as I...)
It should also be up to society to organise the education so that those who didn't show their potential during basic education can still have ways to earn access to higher education. High school grades, as noted in my point 1, don't necessarily show intelligence, and some people from disadvantaged schools have been shown to have the smarts and work ethics to become top students in college, if allowed to try for it via a separate selection that don't make them compete with high-class students, despite the initial disadvantage of a lower level basic education and general culture.