If a site has been configured to display PHP notice/warning/error messages in the logs only (not on the screen), Drupal should respect that setting. But currently it ignores that on update.php and always displays them on the screen.
This can cause confusion for people who are not used to seeing such messages in the admin UI but then suddenly see them when they update to a new Drupal version and run update.php. I suspect (but am not sure) that this kind of confusion is evident in some of the comments at https://www.drupal.org/node/2487215.
Before I looked through Git history to figure out when/why this behavior was originally added, my guess was that it was probably added somewhere around 2004 and the likely reason was that update.php wasn't capable of sending messages to the logs at that time. I wasn't 100% correct, but pretty close :)
This behavior is no longer needed, so it should just be removed.