One of the advantages of using a DVCS is the edit-commit-merge workflow (over edit-merge-commit often enforced by a CVCS). Allowing each unique change to be recorded in the repository independent of merges ensures the DAG accurately reflects the true pedigree of the project.

Why do so many websites talk about wanting to "avoid merge commits"? Doesn't merging pre-commit or rebasing post-merge make it more difficult to isolate regressions, revert past changes, etc.?

Point of clarification: The default behavior for a DVCS is to create merge commits. Why do so many places talk about a desire to see a linear development history that hides these merge commits?

People want to avoid merge commits because it makes the log prettier.  Seriously.  It looks like the centralized logs they grew up with, and locally they can do all their development in a single branch.  There are no benefits aside from those aesthetics, and several drawbacks in addition to those you mentioned, like making it conflict-prone to pull directly from a colleague without going through the "central" server.