Why don't the doctors in Flowers for Algernon perform the surgery on a person of normal intelligence?

Dr. Strauss and Professor Nemur never say outright why they don't attempt the surgery on someone with an average intelligence, but there are a few things we can consider. For one, the doctors may have been eager to see if their experiment could genuinely help improve the intelligence of someone who was lacking. Performing the surgery on a person of average intelligence might have presented some conflict because we do not know whether the doctors had acknowledged any limits to improvement of human intelligence. In other words, performing the surgery on an average person might have prevented them from seeing as huge of an improvement as they did with Charlie. There was also the possibility that the surgery might not work or even have adverse affects-- as we see later in the story.
This brings us to an important theme in Flowers for Algernon- the ethics of medicine and experimentation. This story was written in a time when people with disabilities or mental handicaps were considered to not be fully human. Dr. Strauss and Professor Nemur may have thought it to be more ethical to take the risk of failure with someone who was already handicapped rather than to risk impairment of someone who was otherwise of average intelligence. Further, they may have expected to have an easier time convincing a handicapped person like Charlie to have the surgery than they would have with someone of average intelligence. 
We can tell from the story that Charlie is a fairly independent man. He has a job and lives by himself. Though he is capable of making decisions, deep conflicts of ethics such as medical experimentation were not really in his realm of understanding. This story, though fictional, draws upon the real experiences of many handicapped people who have been exploited in the name of science.