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.
It's an entirely different commit at that point. If work has already started in another branch based on the original commit (for whatever reason), it can cause merge problems down the road. Again, you are likely going to suggest that you can just rebase this other branch on top of the modified commit, but that's still sweeping possible merge commits under the rug, and again just because that rebase is usually automatic including that the tree references should be the same doesn't mean it is always automatic or doesn't have dangerous repercussions (including training junior devs to rebase often and giving them plenty of ammo for avoidable footguns).
I'm talking about a single commit PR in Github or Gitlab. If it's based on the latest version of the base branch, then amending it to include the PR number would allow Github to generate a link to the PR page associated with that commit. That would make the merge commit superfluous at that point.
So something like:
git commit --amend
and editing the commit message. This doesn't introduce any further change to the tree associated with the commit.
But because the commit has different metadata after amending, it now has a different SHA and is a different commit.
For illustration, a minor inconvenience of amending the commit is that `git branch -d my-feature-branch` no longer succeeds for the original branch, because it looks for the actual commit SHA, not the tree.
You may not care about the effects of changing the commit, but those effects are real and other people care.
Assuming you were the one who amended the commit before pushing it up to the remote, there's no reason that you would not be able to delete the branch because your local working copy has already updated contents of .git/refs/heads/my-feature-branch.
For those who have cloned the repo for testing, they can simply run git checkout my-feature-branch; git fetch origin; git reset --hard @{u} to get their local repo in sync with the remote.
So there's no reason that amending the commit will affect anyone until they branch off of the repo to do their own work. But that's nothing that a rebase can't fix.