I think it depends very much on how PMs are used whether it makes sense to see links to the inbox in the interface.
To me, it always made sense that those are hidden. By default, PMs are only disabled for TL0. So as soon as the user has spent 10 minutes reading, they can see their inbox. I don’t expect them to receive that many messages until that has happened and I don’t expect them to receive so many notifications that they won’t at least be able to find it in the full list of notifications. For me, this was always part of simplifying the interface for new users.
I don’t think a new user needs the inbox with all these tabs at the top for reading the first few welcome messages. Especially the dropdown for (group) inboxes is not needed by most users. As long as you are not in at least one group to which messages can be sent, there is a dropdown with exactly one option: inbox.
I think visiting PMs right from the notification simplifies the experience compared to looking at your inbox. And a permanently visible link to that in the sidebar makes users looking at that more likely.
However, I understand how hiding the inbox can be a problem on sites that don’t allow PMs even on higher trust levels (or for most groups), because then it’s not just hidden for new users to simplify the interface. But in that case, who is messaging the user?
To me, hiding the link by default as long as the user isn’t allowed to send PMs makes sense. If there are sites that frequently use PMs without allowing users to create them so their users still need access to the inbox, why don’t the admins simply add a link to the inbox to the sidebar?
The link was visible for a short time, but it was removed to match the behavior of the notification menu entry Messages section moved to single sidebar link - #4 by Moin