Implement mode for taskbar that allows pausing programs but also stores and shows the latest available thumbnail.
The taskbar should show the latest available thumbnail instead of changing it to the app icon.


-Compositor's settings have Keep window thumbnails options Never, Only for shown windows and Always. 
Setting it to always shows a hint that says something along the lines "Always showing window thumbnails disrupts minimized state of the windows. Hence some windows won't stop their work when minimized."


-So, selecting the option Only for shown windows is required for some programs like games to automatically pause their sound and graphics when they are minimized. It is probably quite popular choice as many people don't want to hear a game when they Alt-Tab out.


-This, however, is quite restrictive as it disables thumbnails for every minimized window. 
Now the thumbnail for minimized window is just the program icon, which is normally already visible on left of the program name (hence of no use). Latest thumbnail, even if not completely up-to-date, would be much more helpful.
As I see it, the whole idea of thumbnails is to help identify the program window and that would be especially important for minimized windows.
Maybe the mode should have a hint in compositor settings saying "thumbnails for minimized windows may not be up-to-date".
Also, is it possible to detect paused programs and have only their thumbnail generation paused?


-e.g. Microsoft Windows seems to mostly show the latest thumbnail