many times, the term cost sensitivity is misnomer, as the damages are caused to semiconductor materials ,in a design, much faster than the time delay of either thermal fuse, or circuit breaker. Even some of the circuit breakers are also depending on thermal devices.
Perhaps we need to trip power much faster than possible damage to the components involved in design.
. Thus trip based on measured current might, IMHO, would be safer. However, the design should be resettable but not demanding fuse or other material replacement.