However, even if I stipulate to that, the result is that Senators are accountable to the party leadership and do toe the line, which is not significantly different than them being beholden to the party bosses.
So the worst case is no change from what we have now, and the best case is that the Senators become more responsive to the concerns of their state.
Plus, you get all of that money that would have been used to directly influence the Senators via campaign contributions now made to indirectly influence at worst (if as you say it would just get pushed down locally) or out altogether at best (which could happen if the cost of trying to buy all of the people needed in the state legislatures with campaign donations was too much to even try).