It created one of the most used statements today, “If we can put a man on the Moon, why can’t we (fill in the blank)”
And the answer to that question is usually “We can. Do we want to?”.
There’s no doubt the urge to “not fall behind” militarily is a contributor to progress. The two world wars contributed a huge amount to aircraft technology, for example. When the DC3 was first built, it was running rings around complacent peacetime military; by the end of the WWII, there were pressurised, massive 4-engine aircraft and jet engines. Similarly, penicillin was a lab curiosity until the war came along.
So everything the space race gave us might have happened eventually. But, it got there sooner because of the government push.
The $2000 toilet seat was a throwaway line, sorry. But it does point out another, different issue. Everything in the space race, and hi-tech in general, is massively over-engineered. What, nobody ever created a toilet seat for a aircraft before this? Couldn’t just adapt the B52 toilet? Or the 707 passenger model? Orions are IIRC prop craft, they aren’t pulling barrel rolls in dogfights. But because the money was available, and they could use it, it seems they design a new toilet from scratch. Why do we know the cost anyway, why is it broken out or a spare part? Did the design fail and they needed to replace the seats? (Who’s the guy who gets to boast the pinnacle of their aeronautical engineering career was designing the Orion toilet?)