I thought that safety lines on ocean-going yachts would be made of webbing rather than rope. I don't know what gave me that idea, it may have been the following entry from the coroner's report on the Sydney to Hobart Yacht Race:

(http://www.equipped.org/sydneytohobart.pdf)

...
THAT GLYN RODERICK CHARLES DIED ... WHEN THE LANYARD WHICH
WAS ATTACHED TO HIS HARNESS FAILED AT THE
STITCHING, HE THEN BEING WASHED OVERBOARD ....

"Stitching" sounds more like webbing than rope or cord; however, I'm not a sailor and may not have understood it correctly.

I agree that the ability of the rescue hook to cut rope would appear to depend on the diameter of the rope and whether it fit inside the hook or not.