Indeed, it would - and that's why some of the most popular messaging platforms in use today (i.e., WhatsApp) have recently introduced the ability to "unsend" any message dispatched via its mobile chat application for up to one hour after the message had sent.
WhatsApp lets you do it - if you've sent a message by mistake, you've got a window of time within which you can delete it. As Facebook writes, the feature may be useful "If you accidentally send the wrong photo, incorrect information, or message the wrong thread". The users will be able to delete messages sent within 10 minutes. At least, that's how its worked for users whose name isn't Mark Zuckerberg.
According to BusinessInsider, the new feature was spotted in the release notes for the newest Messenger update, but for now it's still listed as "coming soon".
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Conflicting message aside, it would seem like a pretty tight window, compared to the implementation by other apps.
Google supports an unsend feature in Gmail although that works a little differently as it holds a message for 5, 10, 20, or 30 seconds during which you can change your mind.
At the time of the discovery, when editing messages already sent in a conversation, the "Unsend Message" option will appear.