According to "Screen Damage: The Dangers of Digital Media for Children", which I recommend, there is no scientific evidence of kids without access to phones being more sad, depressive, etc. But there is evidence of the opposite.
Yes: absence of evidence is not evidence of absence. But it still makes your decision easier.
Jonathan Haidt has assembled a very strong body of evidence demonstrating the mental health harms of allowing access to smart phones and social media for young children.
Very easily: the book does not get moral at all. It just claims that there is scientific consensus about the damage that leisure screens make. This is quite easy to debunk, if false.
Yes: absence of evidence is not evidence of absence. But it still makes your decision easier.