I thought that the point of the Senate was to ensure that each State had an equal voice in the running of the country, regardless of how sparsely or densely populated it was. Thus the focus of the Senate on matters regarding the nation as a whole, while the House focuses on matters regarding the governance of each citizen (and thus is proportional where the Senate isn't).
The existence of the Senate is owed to small states refusing to join the union; it was never part of some grand vision. Here are a couple famous quotes from the delegates:
“If the minority of the people of America refuse to coalesce with the majority on just and proper principles, if a separation must take place, it could never happen on better grounds.” – Pennsylvania representative to small states delegates
“The large states dare not dissolve the confederation. If they do the small ones will find some foreign ally of more honor and good faith, who will take them by the hand and do them justice.” – Delaware delegate
The system we have is a reworked combination of the New Jersey Plan (which favored smaller states -- "one state, one vote," I believe) and the Virginia Plan (which said representation should be apportioned to either population or tax revenue). One of the ironies is that New Jersey's population would eventually exceed Virginia's, but the states' positions were only based on moral principles when it was convenient. Right now Democrats favor appointing a new Supreme Court Justice, but they would surely be more hesitant if the circumstances were reversed.
After settling on a bicameral legislature, it was agreed tax bills must originate in the House of Representatives. As predicted, tax revenues
really are redistributed from some states to others (as SG points out). Population density is probably a bigger factor today as western states tend to be relatively large.
The Senate was definitely seen as a counterweight to the threat of "excessive democracy," and Senators were not even directly elected by voters (changed, of course, under the 17th Amendment). Also, the fact only a third of Senators are up for re-election at any given time makes the government more resistant to sweeping change, along with separation of powers and federalism. Again, however, the main purpose of the Senate was always to secure more power for smaller states. What we have is just another compromise like three-fifths or ending the slave trade in 1808 or never taxing exports.
It probably made more sense before the Civil War shifted authority substantially towards the federal government and away from the states. I sometimes wonder if any of the colonies would have ratified the Constitution, if they suspected it would lead to the kind of over-arching federal authority we have today.
I sometimes wonder if we'd better off had Britain prevailed. They outlawed slavery thirty years before we did. Australia, New Zealand, Canada are well-developed and free. In fact, I'd say they're better in a lot of ways.
