That's a bad argument when you think about it. The US went to the moon as a technological pissing contest, then when the contest was over stopped playing the game because the american government was never interested in getting to the moon, they just wanted to show everyone else how good they were at pissing up a wall.
In terms of space technology we've gotten a huge leap forward by working together, old satellites tended to be huge and extortionately costly(as in costing millions each), most satellites now tend to be boxsats, they're tiny breadbox sized shells loaded with electronics sent up in bulk by a range of companies.
The price dropped, the number of satellites has risen and now we're getting photos from orbit in the order of terabytes a day, we've got satellites telling us what the supply of oil in China is days before China realise they have a shortage and need to import it.
That's all down to working together, lots of smaller companies agreeing to share the space and weight a rocket can send, everyone gets more out it(admittedly it still costs about half a million to get your boxsat in orbit, but that's compared to tends of millions previously).
We've gotten infinitely more benefit as a society out of modern satellites than we ever did out of the missions to the moon, we have rovers on Mars doing the job that it would have taken multiple moon missions to accomplish without the risk of life, we're just not doing stuff for the sake of being first, we're doing what we think yields the best information at the lowest risk.