I admire the attempt to make a logical argument against these laws taken at face value, but I can't help think that's giving them too much credit.
These laws have spread like wildfire around the world with many countries and regions rolling out similar legislation within months of each other, despite the stereotypical lethargy of any and every legislature. That's not the work of some popular uprising of parents clamouring for age verification.
I fear debating the merits of the argument is missing the point; they don't care. They don't care about children, they don't care about the argument, they just want the control.