It didn't take a moon landing to win the Space Race - by that point Soviets already exhausted their potential gained by surprise and trophy German tech, and stopped trying.
It didn't solve any scientific or exploration goals because by 1969 it was abundantly clear (unlike in 1961) that there's nothing to do for people in the Solar System - U.S. Mariner and Soviet Venera probes proved that it was sterile and incapable of supporting life. And lunar flights were seen as a precursor and ways to debug tech for future missions to Mars and Venus - that were not to happen.
Progress in computers, automation and sensors turned out to be so much faster than anticipated that by 1969, while it wasn't yet possible, it was clear that tech that will enable same or better scientific results on the moon but without people, was just a few years away - it never happened on the Moon simply because that job was done by Apollo - just at much higher cost and risk.
CCD camera was invented in 1969 and it was the final nail in the coffin of Lunar exploration, making the "Lunar telescope" a totally laughable plan. Just imagine, in 1961 they anticipated people flying there and back to collect photographic plates or film from the automated telescope - which as they presumed, had to be there because stabilisation of attitude in orbit with precision necessary to make astrophotos, was impossible and it had to stand at firm ground! Needless to say, by 1969, it was possible and sensors to replace film existed too, and Hubble Space Telescope project started in 1969 itself.
Manned spaceflight is a waste of resources and only continues to exist because of institutional inertia.
