I don’t think that’s true. Look at China and Russia. They’re both corrupt as hell, neither country is poor in itself (though a vast number of citizens are) but there’s money galore for many people.
As for states voluntarily erasing corruption, Lee Kuan Yew erased most of the crippling corruption in the early days of Singapore. According to an elderly Singaporean I know there, this was the #1 policy back in the day - he created a body to stamp on it, and stamp on it hard. At the same time, create a standard of living for all the people that is so good that they aren’t inclined to indulge in graft. It largely worked, but for it to work, the leader had to be very strong indeed - to the point of being undemocratic - as well as unassailably idealistic.
In Hong Kong a similar policy was adopted with the Independent Commission Against Corruption, which at one point lost its chairman - due to corruption. Despite this, it does a reasonable job.