There is actually an elegant workflow possible for this as is. If you bind a custom shortcut for the Edit Pivot tool, you can hit that shortcut once, edit the pivot, and then hit the shortcut again, and thanks to the way Studio’s tool selection behavior works, the tool you previously had selected will be selected again.
They aren’t “discarded” (they would still be there if you ungrouped the model), but they aren’t used in computing the pivot of the new model. The Group command just uses the center of bounding box as the pivot when creating new models.
The pivot indicator is rendered in 2d, so it’s always the same size on the screen.
I’m interested to see how many people bring this up. You can’t right now, but the current color is one that is pretty unlikely to clash with the color of the content being edited. I didn’t run into anything in testing where I had trouble seeing them.