> Piping curl, means you can't be sure it came from the author's site.
Assuming you take the same precautions you'd take with any other software download (like using https), there's no difference between curl-piped-to-sh and clicking on a link to a rpm, deb, exe, or anything else.
> It means a broken connection is a broken install
Not if the shell script is written correctly. And if you can't trust the source of your software to get that right, then you can't trust them to get the regular installers right either, so there's no difference here either.
> Don't install random binaries either
No one's advocating for random binaries, but you do have to install binaries from time to time, no? Or are you getting your CPU microcode updates in source form too?
I get it, it's a knee-jerk cargo-cult reaction to flame folks who don't see the huge issue with piping a https URL from the software's main web site to the shell, but if you actually think about it, it does not have the major flaws that you claim it does.