We all know that the Soviets basically gave up any hope of landing men on the Moon after Apollo 11 touched down. This was due partly to the fact that they didn’t have all the kinks worked out of their N-1 rocket, and a loss of will on the part of the political leaders to continue in the face of such failures. But supposing they had the will, and they actually managed to achieve a successful landing and return to Earth shortly after Apollo 11. What would have been the US response? And had the Soviets continued to match the US landing for landing, even managing to avoid an Apollo 13 style disaster, would we have quit with 17? Or would we have gone on with 18, 19, and more? Even establishing colonies on the Moon to keep us ahead of the Soviets?
I realize that there were all kinds of social considerations which caused us to quit after 17, but had the Soviets gotten there after us, would those considerations have been seen to be equally important? Or would we have said, “As long as they keep putting men (and no doubt women) on the Moon, we’ll match 'em!”
Personally, I think that the Space Race would have continued and instead of us blowing our money on nukes during the Reagan era, we’d have been busying trying to colonize the Moon, and perhaps landing men on Mars, just to keep ahead of the Soviets.
Actually, I think we probably would have progressed as the OP suggests. Instead of a Nuclear race, maybe a Space Race would have been better for us. Consider how much NASA has done for us with about 5% of the defense budget.
Frankly, I think it could have been quite a romp. I think the Russkies were actually far better set up to exploit lunar exploration than was the United States.
Both the Saturn V and the N-1 programs used the brute-force “direct” theory to get to the Moon and back. But the Russians were already working hard on setting up orbiting space stations. Possible offshoots from an ongoing lunar program might have led to manned construction/assembly facilities in LEO, a manned orbiting facility around the Moon, and an actual continuously-manned base on the Moon. Because they expended most of their effort on the Apollo missions, the United States might have found themselves playing a little bit of catch-up, but not too much. Witness Skylab, the best space station built yet, IMHO. Space stations, and the technology that comes with them, are the key to manned exploration of the solar system. Big, phallic rockets really only impress the rock-bangers.
The obvious ultimate goal of a continued manned space exploration pissing contest would have been Mars. It was an actual stated objective of the Soviet space program.
Such speculation ignores something that should be obvious to us now. Space stops paying off when the political benefits stop paying off. America won the race to the moon, proved their technological superiority to the developing world, and sent the Commies on their way to the dustbin of history, whereupon we wound up with a fleet of decades-old Edsals to play with in LEO. (Yeah, I know that’s way simplistic.) Americans proved too daft to realize that by advancing manned space technology, they helped make many of today’s technological wonders, like the computer you’re reading this on, possible.
Whether or not competition from the Soviets would have kept up the political payoff, and American interest, is highly debateable. But if it had, Stanley Kubrick would have been a lot closer to the truth than he’s proved to be.