It seems apparent that your local authority will have the last say here. I'm a little surprised that these are considered to be metal extension cords. Perhaps we're not talking about the same product, the 6 outlet plastic PC style power strips are something different.
110.3 specifies that UL equipment will be installed to manufacturers instructions. I have never used multioutlet surface raceways which did not have specific instructions including the use of fasteners. Yes they get fastened to the bench even if the bench has a drop cord to it. Here, anyways.
380.2(B)(2) States that it is not permitted to install where subject to severe physical damage. This leaves it open to interpretation, and my local inspectors take that to mean - okay, screwed onto the back of a benchtop in a laboratory, not okay where it is loose.
The labs I've seen have invariably tried to use it as a substitute for fixed wiring. It is not a substitute for fixed wiring. The last workbench I had made, had a 1/16" steel tabletop. The top extended out over the frame to protect the (in this case, T&B) assembly, which was fastened along the front edge of the frame. Worked great and no questions asked.