I have only ever heard and seen of a "glowing connection" in improperly wired houses, but I have heard and never seen a small length or segment (even a couple inches) of Metal Clad cable that was glowing due to a fault, is this a common occurrence? One should assume even a standard circuit breaker would halt this activity.
Welcome to the Forum, lostoptimism.
Your OP (opening post) asks only about Metal Clad cable. Metal Clad cable is Type MC and has its own Article in the NEC. Metal Clad cable is not Armored Cable, Type AC. BX is a jargon name for Armored Cable and is not, and never has been, used in any version of the NEC all the way back to 1913 (I can provide images of original
Code pages). Most Type MC does not use the metal sheath as the sole Equipment Grounding Conductor (EGC), although there are a few exceptions. Most Type MC has an green insulated EGC that is bonded on both ends to the boxes that the MC cable is connected to. Fault current originating at the boxes, devices or utilization equipment (if bonded), is going to flow in both the sheath and the green EGC.
Think about that. Green wire type EGC in parallel to the conductive path that is the MC sheath. . . Then think about applying a current to these "normally non current carrying paths" of a high enough amperage to get the MC sheath to "glow". . . The Green EGC is the same guage as the Hot conductor. . . the hot conductor is designed to carry the circuit current (let's say, 20 Amps) without heating so as to endanger the insulation on it. . . so, the Green EGC can handle 20 Amps with minimal heating, AND it is in parallel with the MC cable sheath which means the sheath and the Green EGC DIVIDE the 20 Amp current into lower values.
Bottom line, to get a current HIGH enough to get an MC sheath to "glow" means there is something REALLY wrong somewhere else, maybe several places, to get that current.
Now, with regard to Armored Cable, there are reports of "glowing sheath". Many are apocryphal. . . some, few, are based upon good analysis.
I, like Infinity, work in a large area (a different one than Infinity's) with tens of thousands of buildings and homes wired before the Late 1950s with non-bonding strip "BX" Type AC Armored Cable, and it has been and still is a basically stable wiring method.