1. I don't know about "main" motivation - it's hard to say just exactly how the matrix of concerns played out in Paine's mind.
There were senior NASA managers who were deeply concerned about the safety risks of continuing to fly lunar missions. I think if it had been up to Bob Gilruth,
NASA would have stopped after Apollo 11:
Even before the Apollo 13 accident, some senior NASA managers had wondered how long they could get away with the grave risks posed by going to the Moon. Given all of the different aspects of a lunar flight—from the Saturn V launch vehicle, to the Command and Service Modules, and finally the Lunar Modules—an awful lot of very complicated components had to work just right for mission success.
At the outset of the program, NASA had formally established the target probability of overall success for each Apollo mission—a landing and return—at 90 percent. Overall crew safety was estimated at 99.9 percent. But a 1965 assessment of these risks had found that, based upon the current plans and technology, the probability of mission success for each flight was only around 73 percent, while rated per-mission crew safety sat at 96 percent.
Few people lived day-to-day with these risks and concerns more than Robert Gilruth. His fame may have receded in recent decades, but Gilruth stood above all others in America’s efforts to send humans to the Moon and back. After NASA’s creation, the fledgling agency had turned to Gilruth to lead the Space Task Group to put a human into space before the Soviet Union. Later, after President John F. Kennedy called for Moon landings, that task fell to the Manned Spacecraft Center in Houston, which Gilruth directed.
...Gilruth had no illusions about the challenge of reaching the Moon. Moreover, once Neil Armstrong and Buzz Aldrin stepped onto the Moon before a global television audience, NASA had achieved Kennedy’s mandate. If each mission had a one-quarter chance of not landing on the Moon and a non-negligible chance of losing a crew, why keep at it? That feeling only grew within Gilruth as NASA accomplished more Moon landings.
“I put up my back and said, ‘We must stop,’” Gilruth said. “There are so many chances for us losing a crew. We just know that we’re going to do that if we keep going.”
And Gilruth was certainly not alone in this fear.
(I'm not saying I agree, just noting what we know about how managers like Gilruth were thinking.)
All that said, I think budgets were a very big motivation for Paine. I think he was aware that the hardware was all paid for; but it seems he was looking for some sacrificial lambs for the Nixon Administration, to improve his positioning in the fight for the post-Apollo HSF architecture for NASA.
2. The numbering of cancelled missions can be a little confusing!
There was enough hardware to execute Apollo flights to the Moon up to Apollo 20, as things stood in 1969.
In January 1970, Paine cancelled Apollo 20, because he needed a Saturn V to launch Skylab, and he was not in a position to order (or terribly interested in ordering) any additional Saturn V's beyond the batch of 15 launchers already in the pipeline.
In September 1970, he decided to cancel two more Apollo lunar missions. The ones he actually cancelled were
Apollo 15 and
Apollo 19. Apollo 15 was at that point an H class mission (like Apollo 12, 13, and 14); Apollo 19 was slated to be a J class mission, with the improved LM that could sustain stays of up to three days and included the lunar roving vehicle. Of course, he still wanted Apollo 15's crew (commanded by David Scott) to be next in the queue, but they'd have to have their mission profile changed. This meant changing Apollo 15 as it stood into the first J class mission (originally meant to be Apollo 16), and renumbering the remaining missions (17 and 18) to 16 and 17. Which meant there would be no Apollo 18, since its hardware and slot were now taken over by Apollo 17. This made David Scott's crew pretty happy, but was obviously bad news for the crews of Dick Gordon and Fred Haise...
As it turned out, of course, the Saturn V's, CSM's and LM's for those two cancelled flights ended up never being used, save for the original Apollo 15 CSM (CSM-111), which ended up being used for the Apollo-Soyuz Test Project in 1975. On the other hand, though there were other CSM's in the pipeline which ended upnever being used. There was, in short, no lo lack of hardware which was completed or at least in prospect of being completed with which to fly two more Apollo lunar missions, had NASA really wanted to do so.