In the context of merge vs rebase, I think "clean" means linear, without visible parallel lines. Quality of commit messages is orthogonal. I agree with the poster that this particular flavor of "clean" (linear) has never ever helped me one bit.
I think the obsession with a linear master/main is a leftover from the time when everyone used a centralized system like svn. Git wasn't designed like that; the Linux kernel project tells contributors to "embrace merges." Your commit history is supposed to look like a branching river, because that's an accurate representation of the activity within your community.
I think having a major platform like github encourages people to treat git as a centralized version control system, and care about the aesthetics of their master/main branches more than they should. The fact the github only shows the commit history as a linear timeline doesn't help, either.
In the context of merge vs rebase, I think "clean" means linear, without visible parallel lines. Quality of commit messages is orthogonal. I agree with the poster that this particular flavor of "clean" (linear) has never ever helped me one bit.