the photo shows a white wire attached to the K&T and taped up.

Thisa is not a original K&T splice.

Its time to upgrade....

The picture shows a 1960's era Romex cable spliced into the K&T. It
would be advisable to remove that violation

most K&T homes are filled with such violations and some may be
hidden behind walls etc in places with no way to easily inspect.

Things change over 70 to 100 years. homeowners modify things on the
cheap.

the possiblity of such issues on such a old home are great.

and exactly how would any electrician inspect wiring covered with
walls? remember splices in K&T arent in boxes......

worse K&T was designed for operation in open air. insulation shouldnt
be around K&T/

even if a homebuyer was able to get homeowners insurance given energy
costs today the buyer would likely want insulation which requires a
rewire.

nothing lasts forever K&T is obsolete just like a 1940s car. newer
cars are much safer and efficent