ublue co-maintainer here. I go over a bunch of the reasons here: https://www.ypsidanger.com/homebrew-is-great-on-linux/

Namely we needed a way to complement Flatpak and brew was a natural fit. It’s an ecosystem reason not a technical one. It has everything we need and a good deal of Bluefin’s target audience are already using it on mac. So for us it’s an easier lift to just add homebrew and move on to larger problems. Plus it’s nice that they’re working with the openssf to secure the supply chain pipeline, and it’s nice that everything is in github where we can inspect it, use the same tooling we use for the OS, etc.