I agree. I think the child is indeed sovereign, which is why parents have no such obligation. They commit themselves to the child by choice, by their sense of moral obligation, and nothing more.
It’s sort of like the good Samaritan law, which I think could be compatible with libertarianism.
Here is how I see Block’s argument avoiding the fear of vigilantism argument. People basically don’t tolerate such behavior so they agree to tolerate a certain degree of cops storming into a private home to save the child locked in the basement. They sign up with defense agencies that have such laws and market forces make it difficult to avoid agreeing to such laws.
In the case where a person still refuses to agree to such terms, Block maintains that private police could still storm the house if that is what the market demanded. This is why he says that this “solution” is compatible with the Friedman type anarchism, as well as the Rothbardian anarchism.
Regarding the fear of vigilantism, I think Block would simply say that libertarianism doesn’t seek perfection but only better and more ethical results. Competition would put a healthy check on all such behavior and minimize it.