I am a fan of the Singapore anti-corruption method of paying bureaucrats a lot of money. That way they don't have to have corruption side hustles and you can attract good talent to these positions. Somehow this is more unpopular than widespread political corruption.
According to transparency international, Singapore is one of the least corrupt countries on earth. If a politician could make several million dollars a year just from his job, you could attract major corporation CEO caliber people. Otherwise, why would a highly talented person want to deal with untangling that mess?
This is the very famous in economics theory of Becker and Stigler. The high pay isn't so that they don't need side hustles, it is to make the (small) chance of being discovered and losing their job painful. You pay much above market wages, people will not risk losing their job.
Is it true? Well, maybe. From Van Rijckeghem and Weder (2001):
> ... we find evidence of a statistically and economically significant relationship between relative wages and corruption.... While economically significant, the relationship, nevertheless, implies that a large increase in wages is required to eradicate corruption solely by raising wages... The relationship between wages and corruption is not found in regressions with country-fixed effects which points to ineffectual wage policy in the short run...
I haven't found much better evidence than that, though there is Di Tella & Schargrodsky (2004) with a detailed study on a hospital.