And some random shell script installer is going to better than a dedicated package manager at dealing with the differences between N many distributions and M many architectures?

Sure, some install scripts will be quite simple, but in that case, why do you need to have the install script in the first place? You'd only need it if the installation procedure was too complicated for an `INSTALL` or `README` document.

Not only that, but I always end up with impossible-to-diagnose phantom errors if I start mixing and matching some installations from package manager and some installations from elsewhere (like curl | sh or ./configure, make, make install). I avoid using package managers as much as possible because they do too much hidden, undoable, inscrutable magic behind the scenes that breaks everything when it’s most inconvenient.

That's what distributions are for.

Just write software that is not unnecessarily difficult to package.