What motivated the average voter? What does the average voter know about the state's finances, resources, industry etc, etc.? The people of a state can keep track of local issues better, in terms of what their elected officials are doing, and have a greater effect on their willingness to comply with their wishes. So you hire people with experience that applies to your state.
You seem to be arguing that self-government is just tooo harrrrd and it's better to let the feds run it. That's what the 17th Amendment lends itself to. Do the people of a state have more say-so over their state by directly electing two U.S. Senators or by electing state officials (whose jobs are beholden to voters in specific districts of that state) who then appoint two Senators who must answer to them or be yanked?
It's the same as the Electoral College debate. Does that disenfranchise the people? It keeps the liberal eastern cities from ruling over the rural western states with redistributionist policies.
I remember once upon a time on some discussion board (I think it was pre-FR) someone suggested the idea of having the public vote on the Fed interest rate. Everyone casts a ballot and the rate would be set to the average of all the votes.
Clearly a bad idea in that most people have no clue about how the rate should be set, but also because using an average would encourage people to vote higher or lower than what they really wanted to "steer" the rate to the right value. For example, suppose you wanted the rate to be 4.0, and you were allowed to vote for any number 0.0 to 10.0. If others' votes average 4.5, you should vote for 0.0; if others' votes average 3.5, you should vote for 10.0. Only if others' votes average exactly 4.0 should you yourself vote for 4.0.
An improvement to this system, which overcomes the problem of encouraging people to "exaggerate" their vote (but does not, unfortunately, solve the problem of public cluelessness) would be to set the rate to the median voted-upon value, rather than the average. In this way, everyone who votes above the median gets the same 'weight' of vote as everyone who votes below the median.
In a way, I see the difference between a direct overall plebeiscite versus a multi-level indirect system as being somewhat analagous to the difference between the 'average' Fed-rate vote versus the 'median' one.