This announcement of the new top bar says that the design hasn't been deployed yet to stackexchange.com, chat, or Area 51, but will be. I rely on my network profile page on my phone for easy up-to-date status. If the top bar is deployed there without changes, the notifications will be off-screen and the utility of the page will go way down. This page has no mobile view, only the desktop view. Please keep small screens in mind.
Let me show you what I mean. (Sorry for the size; scaling it down did not do well for legibility.)
On my phone at a font size that's friendlier to older eyes, I'd like to be able to see the red and green notifications and the site list (with rep) from the network profile. I don't care about the other tabs. I don't care about my "about" blurb, the link to my profile in the top bar that you can see the first few letters of, or the stuff currently to the right of that (tour, meta, about us, search). I just care about the dynamic data.
I've never gotten userscripts to work on Android devices, so I can't solve it that way.
I don't care whether this problem is solved by making a mobile version of the page, by pointing out some secret ugly-but-functional page that does this like Shog9 did for the inbox, by not moving the notifications on the network-site top bar, or something else I haven't thought of. I'd much prefer a browser-based solution, but I'm open to approaches involving the Android app if merely visiting the page/app doesn't clear those notifications.