To be fair, this is only true in western countries. It's not true, in for example Russia or China. Or to be more accurate, in Russia and China, no matter how many hundreds of billions you own, you won't be able to bend the party to your will.
Now, it's not a complete overlap between the government and the rich, and there are points where the two sides may disagree - some oligarchs have been imprisoned and killed before. But if you as an oligarch know how to say the right things and associate with the right people, you'll be allowed to do almost anything you want with impunity. It's an incredibly corrupt might-makes-right society where the hierarchies of political and economic power have already settled and aligned with one another. Most oligarchs don't get to dictate what happens in the government, but their arguments are basically the only ones that they even listen to.