Perhaps in some places all the dead wood is under nine feet of snow, but personally, I never felt much use for ANY saw.

My area of operations seems to have plenty of "dead and down" wood. Live boughs can be cut quickly bending them down and a applying a chop or two with a good fixed blade knife, as the OP noted.

Sawing wood can use a lot of energy that may be better off conserved in a survival situation.