I understand that your solution makes sense to you and perhaps to some others, but in reality it really is not that great of a solution, and it is certainly not obvious as you noted. Not only would that never happen, but the issues would quickly pile up and the situation spin out of control where uninformed people were voting and making decisions that they really have no business making.
I'm not a fan of big government or of having a small percentage of people making decisions that effect everyone else, but that is exactly how our system is setup and exactly how democracy works in practice.
The government can, will, and should make decisions without the consent of the governed. You think it takes long now to get things done? If all the state legislatures had to put their $0.02 in even less would get done. Then city officials would start saying their view is important, too. Soon everyone would be saying their voice should make a difference! If only there was a system in place to have each person's voice heard...
The single most powerful tool that Americans have is the power to VOTE. Unfortunately most Americans do not invoke this power because they feel it is useless. Maybe so, but at least those that made bad decisions will be gone in at most a few years anyway, then. If it is really a big issue then there is always impeachment, but to start tying hands up at that level and incorporate more chefs in the already crowded, trip-hazard-filled, hot, sweaty, mess of a kitchen we call our government, well, that would just be making a bad problem even worse.
Most human beings (and all politicians) fundamentally will try to get away with anything they can. Whether it is a spouse cheating or a student copying answers during a test, until someone is caught doing something they know is wrong (however it is you define "wrong" is up to you) they will not stop the behavior.
No one does anything they think is wrong. Even if society deems it to be wrong, they somehow have convinced themselves it is right, because it is necessary, or it is okay "this one time"... The government, as a whole, or as a local office, is not exempt from this. They become their own "person" in this regard, acting in such a way that for whatever reason they think is right.
When it boils down to it, we are better off having that few % making decisions for us than to give each and every person from coast to coast a voice by way of vote for big decisions.