Just for the record: We together have been able to identify that the problem is that the TB/MB palette under some (almost all) circumstances doesn't allow a stack of palettes containing TB/MB to become narrower, only wider. And TB/MB stays wide even after unstacking/ungrouping/undocking. It only resets to its original size after restart of AI when flying alone. This issue has just been fixed for the upcoming September/October release 14.1.1.Simple, because it takes up 2/3 of the width of my second monitor.
I.e. the root cause is not in the fact this palette is not resizable, which was for me somewhat misleading. A number of Adobe palettes is not resizable either.