> Like the early Romans, could we create a kind of social reward that would be able to compete with wealth?

Public service attempts to do this with stability and benefits. In other words, in exchange for power you are promised a comfortable life. This used to work but no longer does because property prices near desirable cities, where the bureaucracies are located, are increasingly unattainable even to well paid bureaucrats. The military gets around this, with much lower pay, by providing lodging for soldiers. Perhaps we should do the same for bureaucrats? The revolving door would have less appeal if you didn't need to plonk down a million dollars to live in Bethesda.