Parents can opt out of having an SSN issued for a child at birth in the US.

Sure, but why would they? I can’t think of a good reason.

Regardless all citizens are eligible and should be given an SSN if they apply.

Parents do all kinds of things with the intention of protecting their children. Not all of it is well-informed.

You don't need an SSN before a certain age, so this isn't weird.

Sure it's weird. It's easy enough to do when the child is born, why wait?

My daughter had her SSN used when she was around 10, and I can't recall her ever needing her SSN as it's no longer required for things like medical insurance, etc.