It might be hard to believe, but for space projects bigger than some scale using people is actually cheaper than sending robots.
The big reason for that is that the robots are very modest in their overall capabilities. With humans, you can't get cheaper than the cost of sending one, or better few, people, but when you cross that line, you suddenly have a lot of functionality for free.
I agree. People underestimate the scientific abilities and flexibility of a highly trained technician, particularly on solid planets and moons.
A human living on Mars could operate multiple geographic exploration rovers at much higher speeds than currently (existing rovers get 0.1mph max). This is the benefit of having a 60ms ping time instead of 6-20 minutes. Plus the ability to troubleshoot, clean off solar panels, run slightly different analyses without needing to build it into the probe 8 years ago, assemble sensor stations, etc.
Yes the mass budgets for manned missions are titanic. But with even half-way good mission planning we can get more science done than the equivalent mass of robots - at least for Mars and the Moon. Food and life support mass for long trips to the outer planets (or shielding for Mercury) mean robots will win there.
The big reason for that is that the robots are very modest in their overall capabilities. With humans, you can't get cheaper than the cost of sending one, or better few, people, but when you cross that line, you suddenly have a lot of functionality for free.