Why not? Physical businesses have liability if they provide age restricted items to children. As far as I know, strip clubs are liable for who enters. Selling alcohol to a child carries personal criminal liability for store clerks. Assuming society decides to restrict something from children, why should online businesses be exempt?
On who should be responsible, parents or businesses, historically the answer has been both. Parents have decision making authority. Businesses must not undermine that by providing service to minors.
Physical businesses nominally aren't selling their items to people across state or country borders.
Of course, we threw that out when we decided people could buy things online. How'd that tax loophole turn out?
It turned out we pretty much closed the tax loophole. I don't remember an online purchase with no sales tax since the mid 00s.