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If no places allowed early (read: pre-birth/pre-conception) signup, then the problem of too few places would be at least partially alleviated because those who were born at the time their parents put them on the waitlist would actually get places within a reasonable timeframe.
I'm not saying eliminate waitlists entirely. I'm saying eliminate putting not-yet-existing kids on said waitlists.
Jumping to the front of a line before you have something to be in line for (a baby, or in some cases even a pregnancy) is what's mucking up the system and making fewer places for those kids who are already actually here.
The problem is too few places.
Once there are enough places, early sign up is preferred. This allows them to plan effectively, e.g. by hiring and training enough people in advance. It also allows parents to plan ahead.
An institution fails to deliver a crucial service and you blame fellow victims.