Scott,
If the BX was installed correctly there’s nothing inherently wrong with it.Unlike knob and tube it has a ground wire in it,and if a fault does happen at least it’s in a metal sheath.It’s use fell off when the first generation of Romex came out(the 50’s?).BX’s biggest problem came from people not being careful enough terminating it in boxes.You have to insert a plastic anti-shorting device(called red devils around here) in the end to keep the conductors from chafing on the metal sheath.Leave this little piece out and then move the cable around a little bit and shorts can happen.Personally I just don’t like anything older than Romex.Copper is a soft material and can really only go through so many heating/cooling cycles until it starts to weaken.
Barry