Most of the cost in such a program is in the capital expenditures, the R&D, infrastructure, etc. Launching an additional Apollo mission is much less costly than a single mission would be. See the inflation adjusted chart below for how the cost of Apollo varied with time. Note that the cost for Apollo peaked in 1968, the cost went down dramatically once the only cost was building additional missions.
In addition, multiple landings were required for a number of missions:
- If there were any significant problems discovered early on, additional test flights might have been required.
- If Apollo 11 had met with the same fate as Apollo 13, no landing would have occurred.
- Doing it once could have been a fluke, 2 or more missions was really required to really demonstrate we had that capability.
In addition, NASA wished to accomplish more science than they could do for a single mission. They wanted to learn as much as they could, to take advantage of it as you said.
Given that there had to be backup missions planned, it only made sense to have those missions in progress. The lead time for building a new rocket was on the order of years, including the training of the crew. Without having a backup mission or two in line, it could have been as long as a year before another rocket could have been built to accomplish the mission. And once you have spent the money, you might as well launch the rocket.
After Apollo 11's mission was successful, many people questioned the continuing use of the Apollo program, and over time the public stopped watching the missions, stopped following the progress, and they almost became routine. Despite the fact that there was more hardware available, the Apollo program was cancelled, in large part due to what you mentioned (The goal was to send a single mission there)