How does this square with regimes like Singapore, which is one of the least corrupt nations in the world yet also an authoritarian, one-party system?
This is because, in principle, everything comes down to the fundamental threat that the people can remove the current government, and the government does have full control over the unelected civil servants. If they keep ignoring appeals, they'll eventually get dethroned.
There's a nice symmetry between this and the fact that the law is ultimately guaranteed by the governments monopoly on violence. They can dethrone you too if you don't comply.
When a democracy works, there can be a very effective balance between the people's leverage towards the government and the governments leverage towards the people.
In an authoritarian regime the same forces are present but they are not balanced in the same way. The people can still rise up and dethrone the ruler through violence, but that is so much harder, and it is mostly offset by the governments greater power of violence. So they can get away with so much more.
The rule of law and checks and balances also means these elected officeholders don’t have arbitrary control, which has a lot of upsides (and produced a professional and effective federal workforce) as well as some limits.
I swear we have a problem where we quantize to caricatures rather than recognizing tuned balance, and control theorists would probably anticipate this means things will start to swing a bit wildly.
Fractional direct appointments are the usual case in any large organization. If you're the chief executive, you don't hire individual department workers, you might not even pick individual department management, you probably pick other "C-level" staff and have them manage management personnel most of the time.
It's more like a captain of a ship than "an ant driving an elephant." Every avenue you have to direct the ship depends on a network of knowledge and relationships supporting steering and operational systems. You don't DIY turning the tanker, you team-turn the tanker because you've learned how to work with a team.
Democratic governments can operate without a plurality of support for the current government, because the population generally supports and is invested in the system of government. When democratic governments fail, there is usually very little danger of violence or economic and societal instability, because there is trust in those systems. Corruption and malfeasance harms trust in the systems of governance which democracies depend upon.
Authoritarian governments depend on confidence in the government to continue functioning. The system of government isn't necessarily trusted, the workers of government aren't necessarily trusted, but the leaders are in charge and doing things. Media manipulation and effective propaganda is certainly an important tool for these governments, but pointing out that it exists doesn't mean that it doesn't work! Propaganda totally does work, by almost all measures. Russia, China, Cuba, Iran all have high domestic support for the government.
Authoritarian governments also tend to be very stable - people know what to expect. Democracies change periodically. The stability and familiarity are key to the trust that authoritarian governments maintain. The protests in Iran prior to the current conflict are a good example of what happens when a government fails to maintain the trust of the people - the arrival of war saved the current regime from falling apart at the seams when Khomeini died of cancer in a few months and a squabble for the leadership broke out amid a collapsing economy.
Also, that collapse you refer to can take an awful long time under authoritarian control.
Furthermore, I’m tired of the false equivalence some people in this thread draw between the level of corruption in democracies and authoritarian regimes. They are simply not on the same scale - if you ever experienced both you would know that.
On the flip side, if nobody else requires bribes but you do, you will surely stick out like a sore thumb. If I don't get paid bribes and I am an influential powerful person, why should I pay you any bribes? Especially for something that is legitimate and a part of your duties?
Rule of law doesn’t address the problem of bad laws (from bad governance).
One key difference is the extent the authorities have discretionary powers. Can they do whatever the consider necessary to do their jobs (until the courts tell otherwise), or do they only have the powers explicitly given by the law? Common law systems tend to favor discretionary powers, but they vary on how eager the courts are to keep the officials in check. Civil law systems can be anywhere on the spectrum, but it's usually a legislative choice made in advance rather than a judicial choice made after the fact.
At worst the person gets fired and is prohibited from public sector jobs at that tier of government afterwards for a period of time while the story is fresh in peoples minds, in the rare case the plutocratic owned media let's such a story come out of its mass media products about the not-paid-for bureaucratic elements of government in hopes of reducing polarization that comes from over-promoting one of the arbitrarily different parties as a means of providing the commoners what Orwell called "Two Minutes Hate" or a means of obtaining cathartic release from the tensions that making them believe they are somehow co-authors of the government to keep them engaged as willing participants.
This explains the current state of US mass media so well...
can democratic societies be corrupt, can autocratic societies be not corrupt this is also true.
accept things as they're, not as they ought to be - one of the fundamental lessons one has to learn to operate in this world.
And then you might consider talking to the local paper to see if it would make a story. Also the crapper tabloids might even pay for the story.
EDIT: commenters are still all referring to Singapore which I remind you is the very rare outlier case.
Singapore has yet to have a leader willing to take over the system, because two of its leaders were the dynasty that created the system. The real test is what happens when someone like that shows up; but even Western democracies face this problem, it’s just that the system has more built in speed bumps to overcome.