What if CEO build other things than planes?
Putting inexpert people in positions of authority is guaranteed to damage a business, as Boeing is now finding out.
Should experts always be in control everywhere or are there limits?
There are downsides to that, which is why we don't do it. You can judge for yourself if those same downsides apply to Boeing.
In the same way, I couldn't say if Boing would need something more closer to a priest or a technocrat.
And the military doesn't run the government. That's also a good thing.
The only way your analogy works is if you think it's a good idea to appoint generals and admirals who have no military experience. I hope you don't.
Anyway, why not under certain circumstances? Already now there are differences between countries what is run by the military and what isn't.
Because someone with no military experience is inexpert. They don't know what they're doing.
In the military a lack of expertise is very likely to result in people dying unnecessarily.
The US army corps of engineers being in charge of levees isn't the only way, for example. A lot of generals don't fight wars. And those who do, are under civilian supervision.
The equivalent here would be the customers.
You need the deep experience of having worked inside the beaurocracy of a huge effort on some tiny piece of the project.
You need the abstract experience of having built a smaller, less complicated version of an entire plane yourself. Think RC model plane here. And yes you should be at least an RC pilot.
With both of those experiences you will be able to extrapolate very closely everything you need to know to be succesful in establishing an engineering culture.