I’ve just thought and have realised that many teens are assigned debit and other cards these days as well as Apple Pay etc. I think the difference for me as a teenager is I was dragged by my parents in 1980’s to B&Q, Homebase and the local diy store every weekend (or it seemed like it!) partly to teach me about what tools I needed to do jobs but also to help choose various items for the house and my bedroom.
I was allowed to buy a houseplant but this would’ve been from a supermarket or the local garden centre (which also sold garden tools).
We did have attacks by teens with knives then but it seemed less common, though my DB and his friends carried pen and flick knives on themselves for protection.
I suppose back then, teens did what they were told and rarely questioned authority. So in one way OP’s DD was right to do this. But on the other hand none of us were there so have no idea of the conversation.
I agree with @Ritasueandbobtoo9 that teens do need to be able to shop independently but I also think shops should have examples of why they’re not allowed in, or why they’re (and other people) aren’t allowed to buy certain items like the liquid used to harm the woman and children in Clapham recently and parents should teach their teens the difference between being rude and entitled and standing up for yourself and questioning authority.
I’ll give a recent example of kids running wild, either last Easter or last summer in our local high street when school ended. Presumably school leavers who’d taken exams were celebrating so running and throwing water and trying to spray things. The local Poundland shop had its door smashed and the teens ran away. I doubt they found the parents to make them pay for the damage. Now that Poundland has only one door open rather than two.