Why do people think that just because someone is a great engineer, they lack people skills and need to be paired with a "leader"?

Why? Stereotyping. But stereotypes are rooted in truth, so it's not totally unreasonable. Kent Beck, the creator of Extreme Programming, ended up consulting with a lot of teams. The problems were always people problems. In a talk, he wryly said, "I went into computers to get away from people, and now I'm a #@%&* family therapist!" That rings very true to me. I started coding at 12, and it was sweet relief from the social awkwardness of junior high and high school, which I was never very good at. Over the last decade I've spent a lot of time learning people skills, and they are utterly different than the technical skills that I picked up over the previous 20 years. But some of that time has come out of my hacking time, so it's a tradeoff. In addition to time spent, there's also natural talent. Some people are just naturally better at dealing with people, in the same way that others are better at code, or better at sports. If you're curious, start with Goldman's book "Emotional Intelligence". That doesn't mean that great developers can't also be great managers, but having high talent in both is necessarily rarer than having it just in one area.

Because if said great engineer was enabled to fully control his own project, he would be tempted to quit his current employers to make his own company, or at least demand an exorbitant salary. "They want to alienate us from the fruit of our own labour, in order to usurp it." This is attributed to Karl Marx, if I remember correctly. It is true though that scientists and engineers often lack people skills, in the same manner that most popular types lack the basic understanding of the fundamentals of science. This is a dichotomy reproduced throughout the educational system, in most western countries.

Not everyone makes this assumption, but a lot of folks do make a generalization that tech folks are "geeks" and not the CEO type. This is because there are in fact a fair number of "rainmen" who may have ruined it for the non-rainman CTOs/leaders. But truly, you are not alone in your frustration. Very large men who are not fat are presumed to be good athletes, and guys in suits are called, well, "suits" for no solid reason other than the uniform. So, you have to overcome this prejudice/generalization with a smile, a personal style and evidence to the contrary.

To be honest I haven't encountered this syndrome. You do hear VCs for example say "who's going to run this company?", which is a reasonable question to which the answer can sometimes be "me". Doesn't have to be some guy with white teeth and a good command of sports terminology. It depends on the kind of company and your previous experience and skill set. One thing I will say is that highly talented engineering and product visionary people are probably more rare than folks who can do a reasonable job running a company.

It could be a power play. More likely it is because engineering is difficult and time consuming, requiring full immersion and specific skills. Managing people is just as difficult and time consuming, requiring full immersion and specific skills. The conflict comes from both parties not recognizing the other's skills.

Manager does not equate to leader.  There are good leaders who are not managers and similarly there are managers who are not good leaders.  An analogous question may be, "Would it have made sense for Michael Jordan to be a coach during his prime?"