Lanyards date back to the days of horse mounted Calvary. It's astonishingly easy to loose a handgun when shooting from horseback.
The recent attachment of the cord as used by recent military units to the belt is correctly called a "LEASH" not a Lanyard. Looks like an old telephone cord.
The proper use of a lanyard involves looping it over the shoulder and allowing the loose end to drape along side the butt of the gun. This keeps it under the arm and behind, and under the grip of the gun. Thus worn, it doesn't det hung up on passing brush, ect. However, it does require shoulder epalettte flaps, with buttons. Hence, the tradition of uniform shirts having epalettte flaps!!!
A well constructed proper lanyard is adjustable, and similarly used as a rifle sling to support. When tensioned correctly, it will indeed lend a bit of steadying support, and will absorb a bit of the guns recoil. With the vanishing of the mounted patrols, and discouraged practice of shooting from moving vehicles, the need for the security and retention has likewise diminished.
Back in the '80's when my agency still issued Bill Jordan style holsters and S&W M65's, we usually had at least one revolver get "lost" over board every summer due to the holsters inadvertently getting unsnapped and the gun falling out when leaning over the gunnels during vessel inspections.
I was on a ad-hoc committee the investigated the possibility of going to lanyards.We shelved the idea when the "old school" Chief retired, and we went to M686's and thumb break holsters. We quit losing guns, too. This was the exact reason I never carried my own gun except for backup, in a secure rig.
Fast foward 20yrs, I used a screw eye to secure the Hogue grips on my M329PD that I carried in a nylon finger snap holster while pig hunting a river from a boat. I used a brass clip to attach a lanyard I wore hung over my shoulder and chest. Worn under a jacket, I never had it hang up, and gave me great satisfaction I wasn't going to loose a $$$$ gun in the drink!