According to Tom The Great :

You have very very good points, but I'm thinking they reflect on the
older BX cable that didn't have the shorting wire.

Frankly, I don't think the teensy little shorting wire is of
much use, if you have termination problems, for example,
the shorting wire won't help.

Besides, in a system old enough to have two prong outlets (as
per the OP's original posting), the cable is not going to have
the shorting wire anyway. It's going to be a highly tarnished,
pitted, gritty, dirty grey color, where the connections are
going to be highly doubtful and the banding may be fairly brittle.
Especially since it wasn't originally intended to be a ground path
for 3 wire devices.

Infact AC is so
recognized as a good ground, if they toss in an insulated ground wire
you get HFAC.

Heh. In Canada, AC armor is so NOT recognized as a good ground, that
you're not permitted to use it as a ground. Period. Here, AC armor
is only considered physical protection. The only armored cable
commonly available here for normal residential purposes is the stuff
called "MC" in the US - contains a full size bare ground wire.

[There are other armored cables of course, but not ones that you'd
use in a home except in exceptional conditions. Eg TECK cable -
suitable for power feeds in corrosive/high physical damage risk.
Eg: mines. Power feeds for portable carnival rides.]

Sure there more qa done, but the jacket becomes the
normal ground fault, and the isolated ground is used for the third
prong for sensitive medical equipment.

Now I doubt this 1953 house has AC with the quality control of HFAC,
but just making a point that AC is good, damn good when properly used,
and installed.

I suspect there's rather more to HVAC than simply a "well Q/A'd AC".
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.