In principle, yes, although the optional base-devel group depends on sudo, as do hundreds of AUR packages, and yet other projects you install tend to just assume you have a sudo binary around. Removing sudo will not break your system, but lead to well-deserved anger towards people not declaring their dependencies. :)

If you're ready to deal with the occasional application or script croaking, and subsequently fixing it, you should be fine removing sudo. I would personally consider building a dummy package replacing sudo, including a simple run0 wrapper at /usr/bin/sudo, to have a clean and transparent replacement.

Since it doesn't come installed by default on a fresh system, my guess would be that you won't break anything fundamental, but this is pure speculation.

I'm on Artix and I have removed sudo after installing doas. I do have a symlink sudo -> /usr/bin/doas in /usr/bin. Have had this configuration for about a year, nothing broke.

I think you would need to blacklist it in pacman... however that is done. Otherwise it might just reinstall. It will probably break some script checks in random places, but it is not really a big hassle there. I get the same kinds of random errors with toolbox and distrobox containers that are often missing packages.

Some lower quality script (like I write) might do a check for sudo without error handling, but most will just test on uname or environment variables as far as I'm aware.

Why do you like this run0 more?

This discussion may be helpful to you: https://bbs.archlinux.org/viewtopic.php?id=296931

I think it depends on the distro, some have it as a dependency of their whatever, but should not be a problem on minimal install distro's or pure Arch itself.

You can also just use the root user and not bother with any of the sudo nonsense.