I'm sorry, but you were the reductionist there. Objecting to the proposal of a system seeking to minimize corruption by stating it would be too ressource expensive, when in fact, in no way is the ressource cost a limiting or major factor here.

It is entirely possible for a society to exist without corruption without any records existing. It may be unrealistic in today's society, it does not mean it is impossible. As I said, ressource management is merely an aspect of the solution, better record-keeping is a plus, but they can always be falsified, numbers fudged, accounting mistakes made.

As for the example of corruption not existing despite any records keeping, you just have to think about a small hunter-gatherer community. What would corruption looks like in such a society? Assuming the existence of a patriarchal group with "traditionnal" hierarchy, an example of corruption would be a young hunter killing a prey, eating parts of the liver before bringing it back. This is corruption because the tribe leader would be the one to have first pick, and distribution rights over prized meat & offal. The youngin just bypassed that and declared that his arrow damaged the liver, hence why there is a part missing.

Corruption is a moral, conceptual problem, not a physical, material problem. It exists because there exist a predetermined code of conduct, rules to follow and social order, and that some people decide not to abide by it.
It is entirely a social problem, with ways to attempt to manage it that can manifest in the physical world, with records-keeping, but is not dependent on the existence of such records keeping, but purely on the moral fiber of the population.

If taking money from the coffers while you are in charge is the expected behavior in a society, can you really say you are being corrupt by doing it?

You can't just reduce corruption & fighting it to a material problem, when it is a much bigger problem of how human being acts in society & how this rewards him.