The moon landing itself, that's reasonably fair. However given the overlap with Gemini (many experiments ended up having to be adapted on the fly), Apollo Applications (like ASTP and SkyLab) and subsequent programs that built off of them, there's quite a lot of scientific understanding and secondarily, technological advancement and international cooperation that couldn't have come as easily from sending robots for a lot of that.
But partly I just disagree with the premise that we gained nothing by someone being the first to the South Pole. No one's going to send well-funded and well-equipped professional scientists until it's proven it can be done. The explorers who have to work on figuring out how to get there contribute to those who come after them with more certain paths. It's like saying we gained nothing by having Gemini dock with an Agena. Sure it was mostly a stunt in many respects, but they had to work out all the math and logistics behind rendezvous that made Apollo possible, and that we now use all the time on the ISS.
But partly I just disagree with the premise that we gained nothing by someone being the first to the South Pole. No one's going to send well-funded and well-equipped professional scientists until it's proven it can be done. The explorers who have to work on figuring out how to get there contribute to those who come after them with more certain paths. It's like saying we gained nothing by having Gemini dock with an Agena. Sure it was mostly a stunt in many respects, but they had to work out all the math and logistics behind rendezvous that made Apollo possible, and that we now use all the time on the ISS.