With the government, your target market is every citizen (plus visitors, immigrants, etc.). The private sector has to create its market by providing a product or service, whereas the government is obligated to provide some products and services.
What incentive is there for government to squander talent and keep itself workforce weak?
Politicians' incentives are not to create effective government, but to keep getting elected. Having an ineffective government satisfies their financiers' desire to have less competition for top talent, and gives politicians an easy problem to campaign on fixing during election season, by never targeting the real problems.
Break some windows so you can claim credit for trying to fix them, and then blame the opposition when it doesn't work. It's a game where everyone wins, except the dupes that keep voting for them.
The southern states where I grew up and went to college both lauded people who were able to secure government jobs. No matter how grueling or toxic a work environment becomes and no matter how inefficient workers become -- everyone stays in those jobs for the pension.
In cities and areas where education in literacy is higher it's as if the market "pushes" that desire out, and the perception around having a government job is largely negative (excluding contractors).
I wish there were a way to increase competition for gov jobs and change the perception of them without resorting to privatization.