This is a flawed argument, because the House isn't proportional to population, either. It's _still_ weighted towards smaller, emptier states.
Words have histories of course, and probably at one point this was a spatial metaphor - maybe some bicameral legislature literally did have one of their higher status body on a different floor than their lower status body. But the words upper and lower when applied to the legislative branch have evolved since then.
In particular, for any bill requiring spending, the Senate can only amend a bill that started in the House. Impeachment must start in the house and is then tried in the Senate. The Senate can't nominate someone to office, they can only confirm a nominee presented by the executive.
Should some states have zero?