In your scheme, you need one person to want to be captain, to support a thousand-crew ship. You'll probably need fifty people to specifically want to be janitors to support that one person. Five hundred to be generic crewmen. A few to CxO. Fifty to be middle managers. And so on.
I'm not sure the ratios work out the way you'd expect. For every person who wants to be a captain, you need an army to support him, and I'm not sure you have so few people who want to be in charge (take any high school group activity: someone always pops out at the "leader" -- by choice or necessity -- even in groups as small as 3. Those groups that don't gain a leader inevitably fail, due to disorder and chaos).
And if such a population ratio does not exist, and the man who wants to be captain cannot be captain, then you have scarcity, and politic.
Even among the "hardcore engineers", who revel in their non-leadership roles, that only holds as long as the system itself does; a bad manager, captain, etc, can completely kill the joy of such engineering, at which point, you find a new leader, or an engineer attempts to become a leader by (perceived) necessity.