The reason the Ariane (rocket) program exists is because the US put restrictions on European satellites if they wanted to launch on US rockets.
I'm all for cooperation, but often times you need a strong alternative in order to negotiate effectively.
I think we were way too optimistic about ourselves as a species. Our cooperation does not last long.
Right now I'm pretty sure Starlink is the biggest customer of a private space launch company. Yes I know it's pretty much the same company but look at the other satellite internet providers that are also using SpaceX: Viasat, Echostar (Hughesnet), Iridium, Inmarsat, Intelsat, Globalstar. That's most of the providers that are out there. This goes hand in hand with commercial space launch, as launches become cheaper and more available the share paid for by private business will increase. This is a good thing! Don't you want a college or even a high school to be able to afford to put a small satellite in orbit to do simple experiments? The only way people are going to get interested in space exploration again is if they themselves can actually do things in space, in person or remotely.
There's no doubt in my mind that part of what's driving China in not just the space race is the fact that they want to beat the US.
China would not even bother with half the stuff they accomplished for space if it were not the existence of a competitive goal. The irony is what the US tried to do to contain them in actuality enabled them.