Your friend brings up a good point
"run by the rich" is relative.
You have to have money to be in the senate/ house / run for president. So the system is set up that yes, poor people can't be politicians.
But unfortunately the "run by the rich" narrative is the baseless lies coming from the left because they believe that the people who have the most money in the nation meet in secret rooms and "buy elections"
Funny, because I didn't get any money in the mail last election. I'll have to send a complaint email to the rich folk asking where my check to "buy my vote" went.