Reasons for getting the rig cut away would be many - they point out that the sinking rig was pulling the stern down. But also a downed rig can slam against the hulls with the threat of punching holes in the boat. If the remains of the rig are swaying around it can pose an additional hazard to those on the boat and impede rescuers getting people off.

As for it truly sinking you'd have to know the nature of the construction and the load it was carrying. There are no sinkability ratings from the CG for a boat that size. The real issue is whether the sinking rig and load being carried can overwhelm any natural bouyancy from construction (foam core in lay up, encapsulated wood, etc.) once the boat is swamped. Add in inboard engines, the possibility that the design had mini-keels, and a bunch of other crap on board and a sinking is a real possibility IMO.

What I think the CG regs should specify is better on-board emergency equipment for dealing with these situations. There are very effective rigging cutting tools for emergencies. On a day-charter sailing vessel you are tempting fate to not have that gear on board. A hack saw just ain't going to cut it (pun intended)...