I have an old house, complete with plaster+wood lathe walls. The master
bedroom upstairs is fed from an overloaded old circuit that I want to
replace with a new branch circuit.

I see two options; NM and amored cable. The NM option is use all NM
cable for feeds to outlets, and at every stud, remove the plaster,
snake the cable past the stud, and put a nail plate in. This would
obviously require alot of patch work and painting. The BX option is to
use all armored cable by removing the baseboard trim, securing the
cable behind it and go up to each recept. from there.

Because I need to get past a few door frames, using all armored cable
seems to make sense. I have seen this trick in several DIY books.

Is there any issue with this approach?