When I click "View all inbox items," if I hadn't joined the Meta community, it will redirect my to "Confirm new account" for Meta. For some reason, I need to have a profile on Meta in order to view all inbox items. This seems like a bug to me. This is minor because it's not that hard to join the Meta community but it's a bug nevertheless, so I thought I might point it out.
The system is intentionally designed this way. The global inbox is stored on stackexchange.com and requires logging in to view. It was too costly for us to maintain separate login/signup systems for Area 51 and stackexchange.com and the systems in those places had not been updated in years before we removed them.
Rather than rebuild and maintain another system for those two codebases that would require additional maintenance every time something changed, we made the decision to use Meta as a hub to allow authentication on them in a way that we could build it and not have to do anything else with it. If something regarding authentication changes, we can make changes once on the main sites and the others will utilize it just fine.
The implementation does have the side-effect of requiring a profile on Meta in order to work, but we believe the trade-off is fair. We have zero interest in going back to separate login systems for those sites.