I am sympathetic to this idea, but I don't think it would work out the way you suppose. Rather than push the interests of state governments up into Washington, I think it would push Federal political debates down into state elections. Do we really want every state senate election to be fought over national issues rather than local ones?
The argument goes that if we do that the Senate appointments will be highly politicized and so on, but uh, that's the way the elections are.
Having the Senate represent the interests of the state governments was a useful check on centralization of government at the federal level.