If you want a better analogy that doesn't belittle senior leadership, try Go instead of Checkers.
One of the keys to successful management and leadership is understanding sustainability. Incremental changes over a period of time beat a huge lift followed by burnout and stasis.
Sustainability is the domain of entrenched/ossified/bureaucratic middle managers, moderating or outright sabotaging whatever BS senior leadership is excited about this month.
I think you are severely discounting the skills it takes to lead people, and you are also making an extremely optimistic assumption that companies in the future somehow would be magically more meritocratic than existing companies, when there's no evidence of the sort. On the contrary, people with great interpersonal skills will continue to advance off of the labour of the people with only great technical skill.
Your glorious engineer's revolution will probably not come to pass if history is any indication.
> If leading people is so goddamn easy compared to software engineering, why do so few engineers want to move into people leadership,
a) because they wouldn't enjoy it as much as their current job?
b) because for engineers, being a manager does not give them status amongst their peer group.
> and why do so many of them absolutely suck at it?
a) citation needed. Is it provable that engineers are particularly worse at leadership than the rest of the population per capita?
b) if engineers tend to suck at being managers, it doesn't show that managerial roles are harder than engineering ones. How good are managers at attempting engineering roles, for comparison?
I am so reminded of Brave New World...
"Alpha children wear grey. They work much harder than we do, because they're so frightfully clever. I'm awfully glad I'm a Beta, because I don't work so hard. And then we are much better than the Gammas and Deltas. Gammas are stupid. They all wear green, and Delta children wear khaki...I'm so glad I'm a Beta"
Somehow, the managerial class and the investor class insert themselves between the fruits of the labour and the engineers performing said labour. And if you think that's suddenly going to stop because the nature of the labour changes, then I think you're mistaken.
Enterprise structures rewards rent-seekers, because they are built by, and controlled by rent-seekers, utilizing disposable labour. The only way a power structure like that can be flipped, is through revolution. Or by forming your own company, out-competing these enterprises.
Every QA person I've worked with that is still in the industry has moved on to almost pure test automation. A few years ago that was more like 30% of the role. Now I rarely do almost any manually testing, except for exploratory purposes and to design the test plan. Also for certain things that don't automate well. These days I do more pure development than I have at any other point in my career. It's been super fun, but still quite a change. I've seen colleagues that were more the business analyst flavor of QA get pushed out of the industry when they couldn't/wouldn't adapt.