On incidents, if we click compose email we have a list of quick messages to show up but they are not listing. This can happen for any tables that you can compose an email via email client.
The reason that some or all of the quick messages are not listed in the drop-down is that that they are either available to a particular group or a user.
This is expected behavior. If you'd like to create global quick messages that are available for all users, you need to have user and group empty and the conditions be met.