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I'm not saying eliminate waitlists. I'm saying make putting children that don't yet exist on the waitlist illegal because it makes children who are already born when they get put on potentially not get into the daycare (or whatever the waitlist is for) at all before they're too old for it.
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. >

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. >

How?
There are 9 places in the daycare. There are 10 kids that need it. How will signing up later change anything about the missing place for 1 kid? >

The one kid will still have to be on the waitlist, but that kid will be at the top of the list because there aren't any kids that aren't even born (or possibly conceived) yet on the list. So that one kid will have to wait less time than would have to be waited if people put a kid on the waitlist as soon as it was conceived (or even before!). >

In both scenarios only 9 out of 10 kids will get daycare, right? >

For a time. Once one of those 9 leaves, the 10th kid will get daycare. If, however, the 10th kid was behind a bunch of non-born/non-conceived kids, that 10th already-existing kid might not actually get daycare. >

Any daycare I've heard about will use all (nine) available places for eligible children. The unborn child isn't eligible, so it won't take anyone's place. Only 9 out of 10 get the service at any time; it's only the order that changes depending on sign-up timing. Or do you have different real-life experience? >

Usually by the time a space becomes available, children who weren't born when they were put on the waitlist have been born, and therefore jumped the line in front of the child who was born before they were put on the waitlist, making that older child wait even longer for a space, possibly to the point of aging out. >

I would agree with you IF there was a mechanism to ensure that there are enough spaces for all born children to get into daycare.  
The fact of the matter is though that, for example in my country but I'm sure in many others as well, if you wait until the baby is born before applying for a daycare, you're almost 100 percent guaranteed to not get into one until the child is a couple of years old.   
Parents do this not out of fun, but necessity. >

And if that was illegal, it would not be a necessity. Allowing people who don't even have anything to get into a line for (a baby, or in some cases even a pregnancy) is a major contributing factor to the long wait times for children who are already born when they were put on the waitlist.
If one daycare is full, then choose another. >

In a lot of places the waitlist exists because all the daycares are full. A position only becomes free when someone stops sending their kid.