And that's what a user ~/bin directory is for then - you don't want to run as root, install in your home.
Installing user-own software, in a user-specific location is fine.
/usr/local is not user specific, and setting the permissions so it is treated that way doesn't stop other software referring to it as a system-wide $PATH.
There is no ~/bin directory on macOS though. Homebrew could create one, but iirc Apple's guidelines discourage creating new directories in the user's home folder. (Which I generally agree is a bad practice, btw, although this might be an exception.)
I guess you could put something in the ~/Library folder, although that's not ideal either...
There's no `/usr/local/Brew` (or whatever directory it uses) either, but it creates it, and it changes the ownership of `/usr/local/bin` to make it writable without a sudo prompt - which is more egregious than creating a `~/bin` directory, any day of the week.
If they didn't insist on using `/usr/local/bin` (which is in the default $PATH) the permissions issue would be much less of an issue IMO (not a non-issue, but less of an issue than it is currently)
Installing user-own software, in a user-specific location is fine.
/usr/local is not user specific, and setting the permissions so it is treated that way doesn't stop other software referring to it as a system-wide $PATH.