From Roger Cicala's blog at lensrentals.com describing his teardown/comparison of the insides of the EF 70-200mm f/2.8 L IS II versus the EF 70-200mm f/2.8 L IS III:
Looking from underneath, though, you can see the plastic posts that we sometimes mention. These occasionally break, possibly from shock during shipping. If the IS is not turned off, the lens group is free to bounce in all directions with only the posts to stop the motion.
Both the version II (2012) and version III (2018) of this lens are identical in this respect.
Just because IS is not active and moving the gyros and stabilising elements does not mean the inner half of the IS unit is not free to flop around inside the lens.
Later in the comments section of the lensrentals blog entry Roger responds to a question from a reader and says:
The proper thing to do is 1) Turn IS off at the lens while the lens is still mounted to a camera. This 'locks' the IS unit in place. If you have IS on and just remove the lens from the camera, then it does not lock and off the camera flipping the switch does no good.
You can confirm by gently shaking the lens; there's very little noise if the IS is locked.
The locked position is safer for transporting the lens. If it's not locked the IS unit can bounce around and cause damage. How big a deal is it? I can't say for sure, but maybe 1 in 1,000 shipments that come back with IS not locked are damaged. But the incidence is 0 in 1,000; or very close to that, with IS locked.
In a DPReview forum discussing Roger's Blog entry, Roger answered the question, "Roger - would that be the best practice for ANY Canon lens with IS? Turn off IS, then remove from camera?"
Yes. We do it with every one. The most obvious 'rattlers' are the 70-200 f/2.8 and 100mm f/2.8 IS, but it's good practice. We think it's so important that it's checked twice: once when it returns from rental, and as the last check again before it's packed for it's next shipping.
That being said, damage to the IS isn't frequent even if it's left off (for example, most customers ship them back unlocked), perhaps 1 in 1,000 shipments, maybe less. But for us that can mean several broken IS units a month.
If Uncle Roger says it's safer with Canon lenses to turn off IS and therefore lock it, I'm turning my IS lenses off before putting them away in my bag or case. YMMV.