Being a politician is expensive; fundraising, free time and access is required to rise through the ranks and get stuff done. Also, especially in the US, there is this issue of campaign donations. Giving to someone's campaign is also participating in politics.
And then there is the issue of becoming part of the party apparatus. At my present university, a state university in the Northeast US both College Republicans and Democrats are near invisible. In contrast, at my previous uni, a member of the Ivy League in New England, both parties managed to invite all sorts of established party members, and they were recruiting for campaigning. Think internships.
Yet here on HN we see the benefits of state universities extolled. They may be cheap, but that's because one of the things you go to college for is to build a network of peers and established figures in your chosen field.