Re: "So, if the motor does happen to draw close to LRA for whatever reason (for an extended period of time), the breaker or fuse would never trip/blow but the cable may burn out."
Two comments:
1. As mentioned by cuky2000, the NFPA would rather have the motor & cable run to destruction & keep pumping water right up until the feeder shorts out & trips if need be.
2. Even on non-emergency motors, the overcurrent protective device provides ONLY short-circuit protection for the feeder, NOT overload protection, which is why Table 430.52 permits overcurrent devices sized at anywhere from 175% to 1100% of motor full load. Overload protection is provided by the overload relay at the starter. This is about the same as for fire pump motors, they simply have the additional *requirement* that the overcurrent device be able to indefinitely carry the locked rotor current, whereas in 430, using an instantaneous trip breaker set at 1100%, you're *permitted* to let it indefinitely carry the locked rotor current (which is usually about 600 or 700%).
There is still an overload device in the UL-listed Fire Pump Controller, as indicated in NFPA 20 7-4.4.
The way the NEC is written, it appears at first that motor feeders are permitted to be unprotected for both life-safety and general-purpose motors. In fact, they are typically protected against overload by downstream overload relays, and against overcurrent by upstream fuses or breakers. I agree that it is somewhat confusing the way it is currently written. The NEC handbook helps understand this with general-purpose motors, and NFPA 20 helps makes this clear with fire pumps.