We are planning to replace the K&T in the attic so we can put in some insulation. Is it possible to leave the K&T in the walls by hooking them up to the new wiring at the ceiling/wall edge? Are we taking too much of a chance to save money and prevent knocking holes in the plaster?
It can be and frequently is replaced piecemeal, but I'd certainly be in favor of wholesale replacement if it were my house.
If we accept "1880s-1930s" as the range of its general use (wikipedia, not any particularly great research effort) it's 80-130 years old. And any impact it's having on your insurance rates won't end until it's all gone.
Plus, you can insulate the walls, too, once it's gone. And you'll have ground wires.