Roman elites made themselves wealthy through service to the empire, but they were expected to use that wealth to serve the public. Individuals who exploited the system to an extreme degree to amass wealth (e.g. Marcus Licinius Crassus) could tarnish their reputation. However, even Crassus died in military service trying (very dumbly) to attain the military glory that was expected of roman elites.
In the modern world, pretty much all responsibilities that the Roman elite served now rest on governments. Billionaires are free to amass obscene wealth with almost no social responsibility. There is no expectation, for example, that a billionaire should provide welfare or build a stadium out of his own pocket and provide free entertainment to the masses. Today's system works only if the rich pay their taxes and governments regulate them to prevent excesses on the level Crassus was famous for.
The rich in many countries are no longer paying much in the way of taxes and are subverting government power to free themselves of regulations. In the case of some countries, the rich are even seizing the reigns of power and undermining fundamental state institutions.
It's a recipe for revolution.