But the problem is that it can disappear at any moment if they betray the ideals of the person that got it. So it would make more sense for people that have one to keep the secret so that way if something happens and there's disappears they can send someone to get another one for that.
It'd be nice if people thought like that but they generally don't think further than their own generation and what will selfishly benefit them.
Besides, it's really easy to bypass the condition the spirits have created. If someone knows what the requirements are, they can just raise a newborn child, who has never heard of the actual conditions to obtain the king's bough and who'd never be told, and ensure they are taught the right values (protect the weak, don't take from others) then send them off to go get it.
So yeah, in retrospect, the main reason for not carelessly sharing the conditions to get past the forest is actually that, unlike what Ex-stick thinks, it'll be really easy to abuse that knowledge. Now, to see if one of the three who have learned of the conditions will actually realise it; Note might if he ever gets past how absurdly easy a task he's failed in the past was for this guy to do. They'll probably keep quiet anyways.