Free-turbine engines (where the LP turbine powers a generator, or a ship's screw, or an aircraft propeller or helo rotor) have another failure mode that must be accounted for: Namely, loss of load. (Prop goes to fine pitch, driveshaft breaks, powerlines severed, etc.) This can cause an extremely rapid overspeed, requiring automatic response to prevent uncontained failure (such as QF32 experienced).
In every such installation I'm aware of, there is an overspeed sensor - separate from the main control loop - that chops the core engine to idle, or maybe even to shutdown. I've worked on a half-dozen different such installations.
If you need details - PM me and I'll tell you what your engine is likely to have in this regard.
And I agree - while low/no oil pressure should ring alarm bells, shutdown should be left to the operator.