Well, there are different views of "appropriate". When you do team development and everything is done via feature branches, it's nice to have merge commits so that the integrity of the each feature development effort is preserved via a merged branch in the history. If everything is flattened, it's harder to see where the branches (standing in for development initiatives) begin and end.
You can't always get fast-forward merges anyway. Long-lived branches with merge conflicts are undesirable but unavoidable in the long run. At least some of the time, you're going to have merge commits even when your "appropriateness" test says there shouldn't be one.
A good clean fast-forward merge of a single-commit PR is fine. But I've also worked at multiple jobs where every merge to the production branch created a merge commit and that's also fine. It adds a bit of complexity to the history graph, but it's not meaningless complexity.
If your commit history is majority single-commit PRs then having additional merge-commits everywhere would be noisy, so in that case it would be too much. I don't tend to work on actively developed projects that match that pattern, though. Most feature development involves multiple-commit branches.
The point of using a "proper" merge commit would be to avoid amending/rebasing the original commit and allow the original commit to live as-developed in the final branch.
The only thing changing in the original commit is to include a reference to the PR number in the commit message. There would be no change to the tree referenced by the commit.
You can't always get fast-forward merges anyway. Long-lived branches with merge conflicts are undesirable but unavoidable in the long run. At least some of the time, you're going to have merge commits even when your "appropriateness" test says there shouldn't be one.