Stuff happens. And its not even necessarily the business end of the saw that poses the threat. I put my saw back on my utility clip after a particularly long cut on a live oak limb a few months ago. When I got ready to descend I put my right hand below my friction hitch to control my descent and felt something unusual. When I checked, my 12 strand had been melted through about 75%. It had caught on the hot exhaust of the 200T.
This from an OSHA report of the fatality of a cement worker who fell from 160 feet when his nylon safety lanyard failed. The lanyard had touched something hot and was partially melted. : "Recommendation #2: Personal protective equipment should be able to withstand the harshest conditions to which it may be subjected on any given job.
Discussion: ... Many materials, including nylon, can be easily damaged in the presence of extreme heat. For this reason, nylon lanyards should not be used where they might be exposed to conditions that could include extreme heat; rather, steel mesh or wire core lanyards would have been more suitable. Personal protective equipment should be evaluated before being used on any job to ensure that it can withstand the harshest conditions to which it may be subjected without sustaining damage that would jeopardize the safety of a worker."
OK, nobody makes a "Chain Saw Proof" lanyard. But protect yourself the best way you can. Saying a wire core lanyard provides a "False Sense of Security" from a chain saw is like saying a hard hat provides a false sense of security from a wrecking ball, or a "Bullet Proof Vest" provides a false sense of security from a BAR (Browning Automatic Rifle, .30-06), or a seat belt provides a "False Sense of Security" from a head on collision at 70 mph. The driver of the car might be doing nothing wrong. But unforeseen circumstance can put your life at risk even if you are qualified and careful. Thats why they call it an "... inherently dangerous" occupation.