Only if the bad guys are the ones you're verifying to, isn't it?

The information leaks: everything causally downstream of the verification is potentially a source of information. Examples include targetted advertising, activity in age-gated communities, etcetera.

Children in adult spaces who do not reveal that they are children are rarely targeted by child abusers; but if children are corralled into "child spaces" (which are functionally ghettos, given how much of society now takes place online), it will be easier to locate and identify them.

Children are far from helpless, when it comes to online threats. For example, when abusive comments are posted on scratch.mit.edu, you will see a flood of warnings and chaff to try to protect other children from the abusive material, while the Scratch Team work through the moderation queue. However, many social media sites are designed to disempower users, so we don't see this kind of thing there: I suspect separating children from adults in those spaces makes children less safe, not more safe.