Does our system of justice put too much power in the hands of unelected officials?
Whether you believe that the United States system of appointed judges puts too much power in the hands of elected officials is a matter of opinion rather than fact. On the other hand, the more an opinion is based on careful assessment of facts, the more likely it is to be convincing.
First, although many members of the judiciary are appointed rather than elected, they are appointed by elected officials, and thus they are not simply parachuted in at random.
The next question to ask is that of expertise. Is the role of a judge to express the will of the majority or to be an expert, like a doctor or an engineer, in a specific body of knowledge? If a judge is intended to be an expert, then only other experts can judge her qualifications, and even congressional review of appointments would be counterproductive.