No I don't. Your reasoning is absurd.

Today I can walk into a shop and buy alcohol without showing my ID.

I can also walk into my local library and read any book I wish to, some with adult themes. I could do this as a teenage too. I also did this in my own school library.

Demanding to see ID to access online content is a terrible idea and it is the parent's responsibility to look after children. It should be an understanding between the parent and child on what they should be accessing online. If that breaks down then the parent should do their job of being a parent. Take the device away and punish the child.