Governments don't refuse to fire incompetent people because of "political law making". They refuse because firing people is hard, emotionally draining, legally risky and something that managers will only do when properly incentivised. Without competition or profit there is no incentive to rock the boat and pick a fight at work, so why bother? Some noble idea of higher quality public service? Fat chance.
My point is that in government, there is a hard divide between the people who make the rules, and the people who implement the rules. The people who make the rules are rewarded for distrusting and limiting the capabilities of the staff.
In private industry, it's the opposite. Executives ultimately are judged by the performance of their staff, and they have great flexibility in how they organize and delegate authority down the chain.
Firing is not the key secret to success. Dictators can fire anyone whenever they want, but as you point out, their governments are not necessarily any better, and in many ways worse, than the U.S.
The staff of government have to work within whatever decisions get handed down to them from the political process. The political process does not always prioritize staff flexibility and initiative. To the contrary, it's a favorite pastime of politicians to play up public distrust of the government.
In terms of government staff, a lot of people go into the government not because it is generically stable, but because it's the only place you can do certain work. If you want to manage a public park, you have to work for a government. If you want to catch criminals (and your name is not Sherlock Holmes), you have to work for a government. If you want to fly fighter jets, you have to work for a government. If you want to create policy and regulations, you have to work for a government. Speaking of the NSA--if you want to legally hack into a bunch of stuff, you have to work for a government.
In competencies one can do anywhere, like deliveries or contract management, I think you're onto something with your idea of seeking stability.
But I think the attribution might be backward. It's not "the government is made inefficient and inflexible by the lower quality of people who work there." It's more like "the government is made inefficient and inflexible by political law making, which makes it hard to attract the most dynamic people."