Do they act as a bonus to the points you start out with for the following quest? I can't find an answer in the book.

There is no purpose. There are lots of theories, but no truly clear answer.

Personally, I think they're awarded for thematic purposes - every time the heroes earn CT it's supposed to represent a step toward completing their quest. Killing the boss/completing the goal is certainly a step in that direction, therefore you get CT.

There is actual one game-related purpose: If the party kills the boss with an attack that kills one or more heros as well (or -as it happens to be in one quest- the boss has some kind of retribution when killed), the 4 CT extra may ascertain hero party victory in most cases.

The first quest in the Altar of Despair expansion (The Thing in the Pit), requires the heroes to finish the quest with a set number of conquest tokens in order to succeed. In this case the conquest for killing the final boss could make the difference between success and failure.

So far I've never yet succeeded at that particular quest, my best attempt ended up being 1 CT short which was agonising. When the nights start to draw in again and we get back to longer evenings I fancy aving another go at that particular quest.

Wow. The fact that there has been no clarity in the FAQ on this issue is funny. I appreciate the help a lot though. Perhaps they just overlooked the redundancy of the rewarded CT. Thanks!