Greetings, brethern.
As the rules on p.190 state, a "Knock-Down" is a half action of the "attack" type. Which means "no other attack actions this round".
No matter is "the Knocker" has the higher Initiative or not, the "Knocked One" can simply use his next half action to stand up (p.192).
So, besides the possibility to inflict damage and fatigue, what good is this action? As far as I can see it, it only makes sense in a 2-on-1 situation where one person of the "team" knocks the single opponent down while the other one follows up as the target is down.
This leave a shale feeling with me, since I would suspect that "once down" it is not this easy to get up. Even in a one-on-one situation, I would assume that you can not get up this easy ones you are down... unless your opponent is a "sportsman" and allows you to.
Greetings
Gregorius