Regarding those comments which effectively argue that most users won't care anyway:
Those red boxes in the docs have made a difference - on this forum, and others I frequent, the fact that ext/mysql is no longer recommended is coming up in discussions far more often. Before that happened, it was apparent that almost no one knew that it wasn't the preferred (only!) API for MySQL.
If you stop to consider that the majority of users don't even know about the docs (they're learning from decade-old tutorials, many of which were inaccurate &| outdated when they were written), then formally deprecating the extension, and adding a Warning in PHP itself, can only be A Good Thing.