Funny, I've been thinking of the same thing since recently repairing something that had a snowball failure mode. Even using a variac at low output voltage, at some point the gear would overheat two diodes in its power supply causing one or both to short out, _then_ the mains fuse would blow. After that happened for the third time, I got sick of it. Had identified the fault, and fixed it, but it was annoying.
Such a 'fuse protector' needs to do more than shut off the power. Since it's intended for use with equipment open for servicing, it needs to fully isolate the mains once tripped. While still being fast acting enough to save fuses in the equipment, and avoid tripping the mains circuit breaker. (To save walking to the distribution board and resetting it.)
That needs an electronic switch (for speed, and able to take full short circuit current), in series with a double pole contactor (for isolation.)
For sensing, a torroidal current transformer. The circuit to set trip point and drive the switches would be easy, I have suitable contactors and CTs, but I didn't decide on the electronic switch part yet.
Since it would normally be used between a variac (and possibly an isolation transformer too) and the equipment being debugged, it would have to withstand the load dump spike from the variac/transformer. So some big mosorbs on the input as well.
For ease of use it should have an analog mains current display, but a digital trip point setting, to allow just typing in a trip current. Plus a reset button, and a very visible "ON" warning light. And it would need its own separate power input, since the 'mains' it controls may be only a few volts from a variac set low. A 12VDC wall barnacle perhaps. Though the electronic switch part would require power rail(s) referenced to the mains.