The dedicated user isn't really required; it just expects that /home/linuxbrew/.linuxbrew exists. That can just be a symlink to your home directory. But yes, creating that symlink requires root on most systems. Brew itself doesn't require root or that pathname; you can put packages anywhere, but then many will have to be built from scratch since the pre-built packages don't work. And you need bubblewrap installed (which requires root) to use the sandbox, but again that is optional.

All that said, when you are running without a sandbox installing to a nonstandard location, not everything works consistently. I run this mode all the time. But it has been getting better.