It's still possible to get children with high abilities even with these events; my ruler's son has stats ranging between 7 and 14, at the end of his education, which is plenty to make him a competent king, even if not quite as superhuman as he would have been otherwise.
You do of course have a much higher chance of ending up with a ruler with terrible abilities, which in my opinion makes the game more interesting.
I don't know if the events affect the AI in the same way as the player; I would assume they do, though I have seen characters in the AIs' courts with abilities of 20 or higher.
Is there a way to mod the event so it does not create a pop-up at all? I don't mind my children's abilities decreasing, but all the extra pop-ups can be annoying.