Only one of the Apollo missions you listed went to the surface of the moon. Apollos 7, 8, 9, or 13 did not go to the moon's surface.
But here's the thing: All of the Apollo missions cited (except, of course, for 13), and the Gemini mission mentioned in the post, were all part of the preparation for the first manned lunar landing. Mercury, Gemini, and then Apollo-through-10 laid the groundwork for 11 and subsequent landings. So did Ranger, Surveyor, and Lunar Orbiter, and so did a host of other unmanned missions which went around and between the Earth and the Moon, and beyond.
The six missions that went to the surface of the moon were 11, 12, 14, 15, 16 and 17. They all happened during the Nixon administration.
Nixon didn't particularly care for Apollo and was no big fan of spaceflight in general. He was willing to bask in a little reflected glory (though, to be fair, what politician isn't?), but had no particular incentive to keep supporting it after the successful first landing.
The landings, moon exploration, ascent from the moon and the docking were all successful and nearly flawless - a little hard to believe considering the list of problems you gave.
Dealing with those problems debugged the systems, procedures, and teamwork for the landings. And the landing missions themselves had their own problems, but the experience of previous missions, the hard work and smarts of the engineers, technicians, and flight crews, and the redundancy and built-in reliability of the systems made them possible. Even so, A11 was almost aborted before touchdown, and A13 was lucky to make it back at all. So it's not like everything magically went smoothly beginning with the first planned landing mission.
Apollo 11 itself could be considered the final test mission of the Apollo program. It had one single primary objective: "To perform a manned lunar landing and return." Science objectives only became primary beginning with A12.