The old system combined them because it crammed them into the Notifications drop-down, which - like the inbox - was implemented as a network-wide queue.
It wasn't exactly a design goal; that behavior made sense for normal notifications and so mod-messages kinda just came along for the ride.
With the new system, we had to break these out - they're entirely too noisy on larger sites to group into the inbox, and they simply don't make sense in the Achievements list.
Most moderators only moderate one or two sites. Any other site they participate on, they're a normal member of the site and should feel free to participate without distraction. We've never done cross-site flags for the express reason that doing so would interfere with the ability of our moderators to ever take a holiday: moderators should be moderating when they're active on their sites, not dragged away from doing something else.
I do appreciate the confusion this can cause for folks like yourself who moderate multiple sites, but I encourage you to just try it out for a little bit first: get past the initial confusion, and see where (or if) it actually interferes with your ability to use and moderate these sites. It's possible (though probably not trivial) that we could come up with a solution to address such problems if we can nail down the scenarios that lead into them.
Note that the one scenario I considered very important was replies to mod-messages that you've sent: those still go into the inbox and are visible network-wide.