I agree with your comment about representatives catering to special interests, bribes, etc. Their constituents aren't usually first or second in priority. Public corruption is a serious problem.

But as for the Senate and Presidency being decided by mechanisms that aren't directly tied to population—that's by design. The United States is comprised of 50 States that jointly gave up some of their sovereignty to become a republic. They're more than just administrative districts of a national government. Aforementioned issues aside, the House of Representatives is supposed to represent the will of the _people_ while the Senate is supposed to represent the will of the _States_. The Senate is the States' representation at the Federal level. (Indeed, before the 17th Amendment US Senators were elected by State legislatures, not popular vote. Part of the motivation for the 17th Amendment was—wait for it—corruption in the state legislatures!)

It may be that moving to more population-based representation scheme would alleviate some issues. It also brings a downside: less populated states would get steamrolled by the more populated ones. (This was the Virginia Plan at the Constitutional Convention.) The 10th Amendment explicitly states that any power not expressly granted to the Federal government by the Constitution is retained by the States (States' rights/sovereignty), so basing Senate representation on population rather than giving each State equal representation would disenfranchise some States.

https://en.wikipedia.org/wiki/Connecticut_Compromise

https://en.wikipedia.org/wiki/Seventeenth_Amendment_to_the_U...

https://en.wikipedia.org/wiki/Virginia_Plan

https://en.wikipedia.org/wiki/Tenth_Amendment_to_the_United_...

edit: formatting