I don't know enough to comment on European countries, but I wouldn't be surprised if access was a big problem there as well. The American healthcare system is pretty bad, but it's not the only bad system in existence. There may be other linked factors like stigma at play as well.

Right. Abstinence doesn't really work in the real world, only in the spherical-cow world where humans are perfectly obedient.

No, that's the strategy for lower-caste straight people. Telling them that leads to socioeconomically capturing a large percentage of them by burdening them with children before they can hit early potential.

Telling people to not ever have sex is different from telling people to not meet in large groups during an acute and temporary pandemic. Especially when you only forbid sex for a subset of the population while the remainder of the population is allowed to have sex. The group ban on the other hand is mostly unrestricted and thus more fair.

And I'm sure transmission rates would be even higher if condoms were harder to get.