You are going to get a lot of people telling you that you're a libertarian nutjob. Even here, which touts itself as a bastion of internet privacy champions and "experts".
But you, you're walking the walk. Asking the hard questions and accepting the consequences. There is only one way to make things change.
Don't let any little pedants tell you "how your daughter is going to grow up", either. Or that they somehow know how she'll feel about you.
FWIW: my kids have SSN's and that is just as dangerous as what you've chose.