As a spinoff, people would continue to be involved in their State level politics, when currently I doubt one person in 10 could tell you who their State (not Federal) Senator or Representative is.
But what was supposed to be a bottom up government has become very much top down, the power in this country was first and foremost supposed to be in the hands of the People. Idiots electing politicians isn't working out so well, either.
The much much more important distinction between the Senate and House than the manner of election was that each state has the same number of Senators regardless of population.
The people of each state are “the state” as much as the state government they elect. No need for a middle man unless you think the career politicians that run state legislatures are our betters.
Anyway, the most important point his that this scheme is a fantasy with zero chance of ever happening and if our side actually made it a major campaign issue it would be extremely unpopular wedge issue.