Is 100-year old armored (BX) cable a safety hazard and should it be replaced?
I think you are over reacting With what you have provided original would be knob and tube it is still legal. BX is much safer If there is an issue it is inside the flexible conduit and that metal conduit is quite a bit of protection.
Replacing breakers may or may not be possible with your existing panel and again your wiring is in conduit so I would not be concerned.
Depending when and Or the type of panel You have we may suggest getting it updated (especially if FPE™, StabLock™, Federal Pacific™ &amp; Zinsco™ are the leading panels that have problems). Some obsolete panels do not have arc fault breakers available but are still good panels.
Note I have seen more problems with skinned NMB than with BX, MC or AC.