Tangent: Homebrew itself doesn’t really
choose to take over /usr/local; rather, it just accepts that there exists POSIX software that is way too hard for most machines to compile, and so must be distributed precompiled; and yet where that precompilation implies a burning-in of an installation prefix at build time, which therefore cannot be customized at install time. And so that software must be compiled to assume
some installation prefix; and so Homebrew may as well
also assume that installation prefix, so as to keep all the installed symlinks and their referents in the same place (i.e. on the same mountable volume.)
You have always been able to customize Homebrew to install at a custom prefix, e.g. ~/brew. It’s just that, when you do that, and then install one of the casks or bottles for “heavy” POSIX software like Calibre or TeX, that cask/bottle is going to pollute /usr/local with files anyway, but those files will be symlinks from /usr/local to the Homebrew cellar sitting in your home directory, which is ridiculous both in the multiuser usability sense, and in the traditional UNIX “what if a boot script you installed, relies on its daemon being available in /usr/local, which is symlinked to /home, but /home isn’t mounted yet, because it’s an NFS automount?” sense. (Which still applies/works in macOS, even if the Server.app interface for setting it up is gone!)
The real ridiculous thing, IMHO, is that Homebrew doesn’t install stuff into /usr, like a regular package manager. But due to macOS considering /usr part of its secure/immutable OS base-image, /usr is immutable when not in recovery mode.
I guess Homebrew could come up with its own cute little appellation — /usr/pkg or somesuch — but then you run into that other lovely little POSIXism where every application has its own way of calculating a PATH, such that you’d need to add that /usr/pkg directory to an unbounded number of little scripts here and there to make things truly work.