When the contextual taskbar got added to Photoshop Beta, I requested a pin function for it, so it doesn't jump to random locations. Very important for muscle memory.
I personally placed it on the top right of my application, near the Windows minimize, close etc buttons. Perfect, because usually there's nothing there in most Adobe apps.
I've not used the contextual taskbar in Illustrator much yet, but I just now found out you can't drag it out of the canvas window. So the tab you're working in, it's always overlapping your workspace. For the same reason as pinning being rather important (for muscle memory), this should also be possible. Honestly I don't get why they have been implemented in different ways across all apps to begin with. But please at least make them them behave the same across all applications, so I can pin them all in the same place, in every application.