The whole “local” vs. “global” time picking is confusing and not needed.
The only analog that has existed to this point has been when you zoom in on a single graph and that timeframe isn’t applied “globally” until you hit the little calendar button in the graph widget. When I use that feature in UIv3, I often find myself wishing for an unzoom button along side the “apply globally” button. I would use both of those buttons regularly. Currently, I use the apply globally button sometimes and other times, i go to the page time picker and reapply the chosen timeframe just so i can unzoom the graph i zoomed in on.
Does that help?