At these scales, and being able to use the hull's weight against itself, that chain is plenty "sharp" just by itself, I guess (sharpness being the ability to concentrate force on a comparatively small surface area). Adding teeth to the chain would probably not be worth it and/or they would just dull or break soon anyway.
Also using an alternative line an abrasive cable would not make sense either. If friction causes it to tear it would need complete replacing, which would be plenty $$$.
Instead, with a chain they just replace a couple of broken links and back on track. Which is apparently what they've done:
> Unfortunately, the chain actually broke during the cutting operation. “Approximately 25 hours into the cut, the cutting chain broke,” St. Simons Incident Response writes on its website. Luckily, there were no injuries and there was no damage to the equipment. The team simply fixed the chain’s broken link, inspected the other links for signs of fatigue, and continued on.
>>> Adding teeth to the chain would probably not be worth it
When the Kursk was raised they first cut it in half using an abrasive chain/cable. In that instance it was pressed down from above the structure.
"A cutting chain made of abrasive covered bushes on a thick steel wire was pulled back and forth across the hull by the cylinders. Vertical forces were supplied by the controllable vertical position of the suction piles."
Yes, I think this is the right intuition. Given the size and weight of the hull, physics is operating at a different scale and “sharp” looks quite different from our daily experiences.
It reminds me of a Fermi estimate that my physics professor presented of how tall the tallest mountain on Earth or a generic planet of mass M could be. He started with the intuition that when the weight of a mountain overcomes the typical strength of chemical bonds, what we typically experience as “solid” rock will behave like a liquid and collapse.