The fist ,closed hand position allows one to punch and or hammer fist.
The hammer fist covers more surface area ,so if one were to throw a hammer fist to the nose,a miss would still allow a strike to the eye socket,mouth,jaw,and deliver such strike with power.
The Ax Hand is a more defined striking area.
If the target moves or the strike is not direct the outcome may not be as desired.
The knife hand ,to me,also allows a strike with an open hand which may then be turned into a grab or hook.
Most tend to find the fist/hammer fist easier to use.
if I may go back to the last post you made about Milling.
I have done milling when I went through Royal Marine Commando School.Milling is Boxing mainly,with the purpose of getting people to fight.
No Finishes or killing technique just hitting and getting hit.
Combat Judo was for confronting the enemy and injuring him badly or killing him,not an aggression builder.(Boxing,Wrestling,BJJ,MMA are better suited for that,that is also what Milling does)
Combat Judo was not sport Judo ,is was Judo brought back to its roots ,Jujitsu.with strikes,breaks and kills.
Same as Bayonet training,it was to learn to use a tool to kill or injure the enemy at close range,not an aggression builder ,though aggression was used to get people to WANT to kill close in.Screaming and running in toward the enemy might cause most to stop and think,screaming sort of blocks out the thinking process and allows one to go forward when they other wise might not.
Pugil sticks were the Aggression building aspect of Bayonet training.Hitting and getting hit with padded sticks with a butt end and a bayonet end.(One on one,two on one,three on one) When you downed your opponent with the pugil stick you finished him off though,you smashed his face in with the butt or stabbed him multiple times with the bayonet end.