I never said while still running, your words, not mine. First step, yes, shut the PSU off (first sentence I posted so I know you just skimmed it). Fire won't magically extinguish flipping the PSU off. Taking the side panel off takes 5 seconds at most.
Again, completely theoretical situation but once something is burning (aka fire) it keeps burning. How are you going to get the cable out with that agressive of a bend?
Or alternatively something else catches fire and you rush to get the components out to save what you can, the card being one of them.
That cover need to be magnetic, maybe it is but the picture doesn't show magnets.