Isn't NASA run by the government? Why not pay people to do their job correctly?

The word "government" doesn't magically erase all the same individual & institutional incentives, ambitions, biases, & flaws that exist elsewhere.

And sometimes, the extant magical belief that "government" is different & immune lets those same human factors be ignored until they feed bigger, slower disasters that everyone is afraid to admit, because (ostensibly) "we all did this together".

Just because you pay people doesn't mean they do their job correctly.

It just gives you the option of not paying them if they don't do their job correctly.

The role of for-profit companies and 'shareholder' value in explaining corporate bad behavior is highly overstated. The only profit that matters is the one at the individual level (i.e., compensation, which is a form of profit, for the individual).

A government employee or a private corporation doesn't matter. To the actual humans, they are the same, in that each provides a particular compensation, tied to their decisions.

Is "Why not pay people to do their jobs correctly?" a way of voicing frustration with massive gov't incompetence? Or a way of saying that organization incompetence is top-down?

Because the grifters are running the show. The point is not to fly to orbit/moon/mars/whatever, but shovel taxpayer money to politically well connected large aerospace contractors.