Earlier quoted context omitted.
Arch has pacman and that worked so well that it had to have AUR which is just glorified curl | bash. Linux distros managed it for decades when the vast majority of binaries you would run are made by nerds for nerds. If the original maintainer isn't willing to securely package it then you're often SOL.
AUR (also PPA which another comment cited) is emphatically not the same as "just run this script". If anything, and at worst, it's analogous to NPM: it's an unverified repository where the package is run at the whim of the author, and it leaves you subject to attacks against or by that author. You still, however, know that the author is who they say they are, and that other people (the distro maintainers) believe tha…
This doesn't mean anything since "who they say they are" is an anonymous username with no real life correlation. Might as well be completely anonymous.
> that other people (the distro maintainers) believe that author to be the correct entity
No? Anyone can make an account and upload to AUR and it has exactly 0% to do with the distro maintainers. Packages can be removed if they're malicious, but websites can also be removed via browser-controlled blacklists (which I don't like btw but it's how it works nowadays).
> And any such compromise would, by definition, affect all users of the repo and presumably be detected by them and not by you in the overwhelmingly common case.
This is true of a popular website that advertises install instructions using curl | bash as well.
I've been using Linux for the past 2 decades and my general experience is that it is in no way more secure than Windows or Mac, just way less popular and with a more tech savvy userbase.