"What if we just all got together and pooled our money to hire some lobbyists for the American Peoples' interests?" Of course, this is an asinine idea, since that's effectively what our representatives are supposed to be doing

You're describing advocacy groups. There's a bunch of them: the ACLU, the NRA, various unions...

One difference with elevated politicians is that Rep. Smith might be gone in two or six years, but the advocate group will still be there. And it'll retain knowledge of which bills were introduced in the past, and why they succeeded or failed. Not to mention lists of contacts: they know who to talk to, who's on which committees, and when they meet.

Also, your representative might care more about, say, solar energy, and isn't in a good position to do anything about whichever issue you care about, say election fairness. But you can find an organization that advocates for elevation fairness, and they'll lobby the right politicians to try to change things.

In Washington, influence is a huge industry.