My understanding is that US government salaries are high because the US private sector pays so well for comparable positions. The US is in the peculiar business of competing with itself, in a sense, or at least with its own economic model.

Private vs. public isn't such a teeth-gnashing, nail-biting dilemma for many other countries, who generally seem to do a better job of mentally separating the two sectors. The general agreement in other countries is that public = stable job, lower pay, higher "public service" calling; private = higher salary, less stability, etc.

Of course, this isn't taking into account countries like China -- where a government position is the best route into cushy, lucrative gigs in the private sector, and in fact, that's often the entire point. (To some degree, this is also the case in the US, at least at the higher levels of public service.) But I digress.

I think the same public/private comparisons for salary, stability, etc. apply in the U.S., at least for some job categories. It's just that, as you said, the private sector pays so well for comparable positions. Salary-wise, I think less skilled position do better with government, but the higher-skilled positions do better in the private sector. If you see a government engineer/scientist/mathematician working alongside a contractor in the same role, the government employee almost always makes less.

More importantly, UN salaries are exempt from income tax: https://careers.un.org/lbw/home.aspx?viewtype=SAL

yes, that's on top of the so called post adjustment that for e.g. Geneva (last time I looked) was around 96% (base salary + post adjustment = net salary (+ normal tax rate) -> gross salary in the private sector (30 working days holidays p.a., up to 70% pension levels (17years contribution) with 5 years+ contributions getting you a pension, for senior staff add no VAT, 50% lower petrol prices, real tax & duty free shopping everyday - about half or less your airport shop, etc etc etc)

...and as salaries are normally paid besides tax free also tax equalized (the US is demanding income taxes from all citizens wherever they live including UN staff - the UN covers these taxes for US citizens and a handful other countries) the US pays itself back (via income tax) a nice discount of certainly 10% of its contributions to the UN.