I’ve moved this to Contribute > Feature, but I do think it’s reasonable to expect that folks who can edit other users’ posts should also be able to edit other users’ chat messages.
I’m not sure it’s been discussed prior to this though, so it may be helpful to pause and think “why not?” as well.
I’d argue, at least, that it’s more important for this feature to exist in posts, where content are more durable and discoverable, and less important for this feature to exist in chat, where messages scroll off the page, and some reply-noise to ask the user to edit it themselves is less objectionable.
Not saying we shouldn’t do this on those grounds, but for those reasons, I’m not yet ready to jump to prioritize this and I can understand why it hasn’t come up yet.
It’s good to hear examples though, and interesting that in your case, @JammyDodger, you chose to delete the message.