The condition of the wire may be a factor, not every device needs a grounded circuit. Sometimes its about as easy to run a new wire for one to the point its needed in remodel. My Dads house, early 60's, just before 3 wire, any additions we run a new wire or modify a couple crucial circuits, laundry, bath, counter tops, lights, switch loops we leave alone as well as many unused 2 wire recepts. Got a lamp in it they never turn on.
As for major appliances I recall they had a combined circuit for range oven, as I recall disconnected it, fed it with the old dryer circuit, it was 240, ran a new 4 wire to the oven and replaced the 3 for a 4 on the dryer. Cost 2 breaker spaces and one cable.