It seems that Furuta's aim was to kill all members of the V and Wasshu clan members who were controlling CCG. So why does he not eliminate both the V and Washhu clans together? Why does he keep Kaiko alive?
Considering the story that happened until Tokyo Ghoul:re Chapter 101, Furuta's aim has been to become the head of CCG (and to marry Rize LOL).
The reason why he killed the CCG head was to become the successor and lead the Doves/CCG so that he can kill all the other ghouls (Aogiri/Anteiku) and in order to do that he needs the external support of V (just like how Danzo did all the dark stuff using the ANBU [Naruto]).
Also if you think of it logically, if Furuta killed Kaiko or any members of V organization, then he would then make an enemy of all the V members along with Kaneki and others. So Furuta is using both the Clowns and V to become the single KING !!