The White Council take death as the first and only option for Warlocks, they seem incapable of putting in the resources to locate young wizards early and their policy of masquerade means that there is no public recognition of the problem.
Realistically, the WC doesn't
have the resources to put in. They're incapable of it in the literal sense of the word.
There are only a few thousand Council-level Wizards. Not all of them are psychologically or temperamentally suited for teaching. Of those who are, many of them already have apprentices, potential Council-level Wizards who need a lot of training and a lot of attention.
The vast majority of warlocks are minor Talents. They have power, and learn to use it and abuse it and it devours them. They becomes dangerous threats to the people around them, to their local communities, etc. But they just aren't powerful enough to be major threats to the world on their own.
The kid the Council executed at the start of Proven Guilty, for ex, was very dangerous on an individual level. He was guilty of murder and rape, it was implied incest and other stuff. He could have gone on to kill, maim, etc. a lot more people if not stopped. But he would not likely ever have been a world-level threat.
The apprentices of the Council members, OTOH, are high-end Talents, and they can potentially be global-level threats if they go bad. So the Council has to focus on them first. Whatever resources go to the minor players have to come from what's left over, from cold necessity.
Now the Paranet and related groups might could fill some of the void. They could identify budding Talents, maybe train/restrain the minor ones themselves and pass the major Talents on to the Council, if that setup could be arranged. Maybe what the Council needs is a setup a little like minor league baseball, with groups like the Paranet as associated groups. But it would be tricky to set that up.
But the Paranet is not really qualified to train the high-end Talents themselves. That's why they would need to have an association with the Council to make the project work.