Steps to reproduce the issue

File administrator/language/en-GB/plg_system_updatenotification.ini has lines:

PLG_SYSTEM_UPDATENOTIFICATION_POSTINSTALL_UPDATECACHETIME="The Joomla! Update Notification will not run in this configuration"
PLG_SYSTEM_UPDATENOTIFICATION_POSTINSTALL_UPDATECACHETIME_ACTION="Set it back to the default setting (6 Hours)"
PLG_SYSTEM_UPDATENOTIFICATION_POSTINSTALL_UPDATECACHETIME_BODY="<p>In your Installer Configuration you have set the Option Update Cache (in Hours) to 0 this means that Joomla is not caching the Update. This means an email should be sent on every page visit but this is not possible. Please increase the value (6 is default) or confirm that the Joomla! Update Notification will never send you mails.</p>"

Hide all system notifications on the Post-installation Messages page. Go to the extensions settings and set the "Updates Caching (in hours)" parameter to 0. Go to the main page - there is no icon about an important system message in the toolbar.

Given that these system messages are generally important, the message counter should have changed by at least 1. This is what I consider to be wrong behavior and created Issue.

Now go to Post-installation Messages and hit the reset button. Hurray, now we finally have a message that says the wrong combination of parameters.

By the way, in the PLG_SYSTEM_UPDATENOTIFICATION_POSTINSTALL_UPDATECACHETIME_BODY constant, I would prefer to slightly change the ending of the phrase. Something like ... or disable the System - Joomla! Update Notification plugin, thereby confirming that there is no need to send Joomla update notifications.