I don't think the "lead solution" is the right one either. Probably better to try to find ways to utilize their particular features if possible while, at the same time, preventing them from reproducing. Realistically, we know that even if a culture came to an understanding about deviants and learned how to find them a place in the world where they could be contained, or their energy redirected, over time, people would forget. Also, due to genetic recombination, it is possible for a line to be started again even if all of a given population had died out.
Most "primitive" tribes would abandon such individuals - even as children - and this usually was a death sentence.
There is a passage in Bram Stoker's Dracula that has given rise to a great deal of speculation as to his source for the remark:
"We Szekelys have a right to be proud, for in our veins flows the
blood of many brave races who fought as the lion fights, for lordship.
Here, in the whirlpool of European races, the Ugric tribe bore down
from Iceland the fighting spirit which Thor and Wodin gave them, which
their Berserkers displayed to such fell intent on the seaboards of
Europe, aye, and of Asia and Africa too, till the peoples thought that
the werewolves themselves had come. Here, too, when they came, they
found the Huns, whose warlike fury had swept the earth like a living
flame, till the dying peoples held that in their veins ran the blood
of those old witches, who, expelled from Scythia had mated with the
devils in the desert. Fools, fools! What devil or what witch was
ever so great as Attila, whose blood is in these veins?"
It's just an example of how deviants were dealt with in tribal societies... but it is interesting because we have speculated that the psychopathy gene is sex-linked, i.e. carried on the X chromosome. That means, it is carried and transmitted by the mother who may not manifest the characteristics at all. Now THAT could create (and does) some horribly tragic situations.
In the movie "The Bad Seed," it is suggested that the child inherited her psychopathy through her mother. The problem with this is that, in order for her to be a full fledged psychopath - as depicted - she would have to have received the gene from her father's x-chromosome contribution also. And if the father had the gene, he, too, would have been a psychopath because he would not have had another X-chromosome (as women do) to counteract its manifestation.
In any event, the situation can be likened to any predator/prey ecosystem such as rabbits and foxes. When there are a lot of rabbits, the foxes have a lot of food and increase. When all (or most) of the rabbits get eaten, the foxes begin to starve or kill each other. Then, when the foxes die back, the rabbits begin to increase again. And so it goes.