See also Matt Yglesias: http://yglesias.thinkprogress.org/2008/12/loser_pays/
The legal system should normally be the last resort, but you seem to be suggesting that we have some sort of universal alternative to try first. There may be other options in specific contexts, for example disputes with service providers in regulated industries where there is some sort of ombudsman scheme, but it is not the case in general.
You mean de-democratize the entire branch of government?
Isn't your comment a general indictment of American democracy in general? Why have an elected congress making policies then?
I would suggest however that in theory, the politicians sell their policies, rather than themselves per se, although they do sell a bit of themselves also. But the way our system works is, you have a philosophy of governance which is conservative, low taxes, traditional values, screw the poor, and the democrats, sort of distribute wealth, keep the companies in check, tax the rich higher, etc. Any one politician in this scheme is not an individual, but rather a representative of a philosophy, or even ideology. So, it is right that the public decides which they prefer at any given time.
However, it would be quite savagery for the public to decide as to who should be guilty of murder, or rape, or conspiracy, or robbery, or the thousands of cases that go through the court. It too would be idiotic for the lay public, with very limited knowledge of the law, to decide as to who should be a judge, a job which requires high intelligence, but also common sense, a sort of moral structure, so taught through law school. Same as it would be idiotic for the public to decide who should be a doctor.
If your judges are appointed permanently by some sort of panel, drawn from some level of politicians, who are themselves elected via a system that is open to trivial interference by well-funded special interest groups, then your judiciary isn't even close to democratic.
It's not democratic - but neither is the process of selecting senior doctors from the ranks of junior doctors.
As far as I know, in the UK and most of Europe, and definitely here in Canada, Judges are appointed by judicial commissions on the basis of strength of legal scholarship, not picked in a popular election based on who can raise the most money and pander to the right interest groups.