We now have Introducing: Comprehensive admin search in case you are not aware, this is much easier to use because it searches everything in admin, not only filtering the sidebar links. Doesn’t help much in this mobile situation, but it certainly makes finding things much easier on desktop.
I did try doing this last year, it ended up being not as simple as I would have thought. We could try again though, it would be nicer at least in admin’s case to show this when you land in the admin interface on mobile.