Corrupt politicians are incompetent politicians. That's my point here.
Competent politicians wouldn't be corrupt. They might not exist, but that doesn't make this untrue.

You're right that what I'm describing is an ideal. But OP asked a philosophical question, not one about today's realities, or at least that's how I interpreted their question.

If politicians were competent, then they would redistribute the wealth from billonaires to social programs that would benefit the people.

That said, I disagree with you on this being unsolvable. Like I said, laws can go a long way. And not everywhere does money buy you everything.

There are countries with progressive wealth taxes on the rich, with the rate going higher the wealthier they are.
Many countries, including rich ones like Switzerland, were in favor of the OECD minimum corporate tax deal until the US withdrew, which would have unfairly impacted their economies and caused every company to pack up and leave. But at least in my country, can't speak for others, it still got implemented except for one aspect which is postponed indefinitely.

But based on the news I've been seeing, isn't New York also taking great steps in this direction? So I don't think it's quite the impossibility for politicians to go against big money even in the US.

Money is powerful in the current world, but it's not omnipotent. You can go against them, and you can create a world where it is powerless. You just need people willing to do so.