Nevertheless I see the much larger problem in the fact that many pairs choose to bring children to the world because this is the action that is encouraged in society (most people are simply conformists). If we could make it the default that it is frowned upon if a couple, for which it will be rather likely "from available data" that the children will be in a bad position in future society, nevertheless decides to have some, I think a large part of the problem would be solved.
I also would encourage children from the bottom quantiles of intelligence or earnings to say clear words to their parents that they are part of their problem.
But it's comforting to know that you wouldn't force sterilization upon them, but instead merely encourage their children to reproach them for having brought them into the world.
Maybe these children could also volunteer for euthanization to reduce the burden on society imposed by such worthless individuals? This would also have the benefit of making the idiotic, conformist parents remorseful for having indulged in their mindless rutting.