It would seem logical in considering the bolstered throat arrangement that hurtling along at great speed on horseback some danger to the rider would be encountered on drawing or placing the sword back in the scabbard...to the hand and fingers. It may be why the design of the Tunkou appears on daggers...in Koftgari only (not the full Tunkou form)
since the Warrior would almost never draw a dagger on horseback ... but would certainly draw the sword pictured above.
Actually when imagining the draw; it is the thumb which assists the backblade out of the scabbard and of course the hand.
Secondly and I favour this;...the sword would fit much more tightly in the scabbard with this bolstering ...Thus the Tunkou as noted earlier has a dual purpose.