You are correct about what the Framers wanted, and what they wanted was tied very much to the concept of a republic. But the elections of 1800 and 1828 changed the focus from a republic to a broad-based democracy. That's why Jackson asked for 3 rather revolutionary amendments in 1829.
Yes, I know and now we’re suffering the results of unintended consequences. I believe the framers debated direct elections of the senators and rejected it. In fact, if I recall correctly, the debate over the makeup and method of electing senators was nearly the deal breaker for the entire convention. It’s a shame the later generations didn’t fight the corruption rather than bastardising the system.