Well I have mine set up so on most there are only 2 or 3 panels, and then I adjust the panel heights so that the tray scroll bar disappears. Then only the panel scroll bars will be normally visible (I use named lists rather than icon grids for inspectors.)
When I do something like open a secondary pane for say the Materials panel, then that is when the tray scroll bar appears, and I know which it is because I just caused it to appear. Often a click on the other panel of the tray (Components in this case as it's my "Resources" tray,) will collapse it, and the "master" tray scroll bar will disappear again.
Re, the images Christina has shown, ... the "Default" tray was never meant to continue to be the way the panels were used. It's just the way that MS suggested that all panels be shown when an application was first installed.
The user is expected to adjust them, create their own trays, sets of tabbed trays, others floating, others auto-hidden etc.
I have my panels divided into a tabbed set of 4 trays docked on the right:
They are slightly different now, ie, detail name lists (instead of thumbnails) and the panel heights are adjusted so the tray scroll bar is suppressed. (And the auto-hidden trays are now docked to the left margin.)
And just for cross-reference, we've discussed these same things in a few other threads:
... so we keep repeating ourselves.