Edit: Both are still extremely cool though
Now, the Apollo program also cost much more than the robotic missions. If you are willing to invest enough (e.g. Apollo was >1% of US GDP/year for most of the 60's) you can get an enormous amount of scientific return from a manned mission, but robots are useful for budgets that can't cover a manned mission.
If your goal is to plant a flag and ship back ~400 Kg of moon rocks, you could do it today, using robots, for a tiny fraction of a manned mission's budget. The thing is, bringing back 400 Kg of moon rocks is not 400 times more valuable than bringing back 1 Kg of moon rocks.
As for "done with 1960's technology" so was Apollo: the ability to discover hydrogen (used to find the ice in the lunar crater shadows) wasn't possible with 1960's sensors that were light enough even for the much larger mass and power budgets of an Apollo spacecraft (vis a vis Lunar Orbiter or similar probe).
In fact, the latter hasn't really advanced at all in those 60 years.
In a similar manner, I would expect any manned mission to Mars to employ a lot of robots: control is much easier when the human making the decisions is a few light seconds away versus 8 light minutes. And if you have the mass (and money) for a manned mission, you can tuck in a bunch of robots for very little extra. So a human mission will always be strictly greater than (in scientific return and cash budget) robot mission.
By the nature of the beast, for the cost of a single manned mission, you can launch dozens of expendable, unmanned missions, that can go on for more than a few days. Robots don't need to eat, or breathe, and they don't grouse when you abandon them on an alien surface.
Meanwhile, people and groups with non-vanity goals are making extensive use of space in 2021, compared to 1969... But that's not very sexy, because things like weather satellites and imaging satellites, and communications satellites and the occasional telescope actually accomplish concrete, useful things, at a fraction of the Apollo budget.
Don't tell that to the Radio Astronomers. Something, something, dark side.[0]
[0]https://www.nasa.gov/directorates/spacetech/niac/2020_Phase_...
"This is but one of many genuinely shocking aspects of NASA's decision a week ago to award SpaceX—and only SpaceX—a contract to develop, test, and fly two missions to the lunar surface. The second flight, which will carry astronauts to the Moon, could launch as early as 2024."
https://arstechnica.com/science/2021/04/five-reasons-why-nas...
I do wonder, however, where NASA would be if they would have continued with the DC-X prototype instead of abandoning it when it had a landing leg failure causing it to topple over in an early test.
> people continue to believe him for some reason.
I believe in him, and the reason is obvious. He gets things done nobody else seems able to.
I'd recommend people to look up into those previous failures (and SpaceX is finding "new ways" to fail)
Make no mistake, if a company or institution isn't trying a lot and failing a lot to achieve a new type of goal, it's also not making much progress toward any new type of goal.
Regarding technical innovation, NASA did a lot of that in the 1960s. There were a lot of failures then (Mercury and Gemini programs), followed by incredible success (Apollo program). NASA's work with SpaceX is another great form of innovation -- pick the most innovative commercial partners and move forward.
Failure during research & development isn't necessarily a bad thing.