I'm with the OP, I've never understood why you'd want to subject your kids to shopping trips, especially supermarkets. It's not weird at all - it's weird to want to inflict boring shopping on tired kids and it's weird to want to inflict tired and bored kids on other shoppers. If the kids enjoy it, nobody would come on here and comment because it would be clear that the kids were happy and engaged doing it. It's not judgmental to comment - and it's highly unlikely that they were miserable because eg they'd lost a relative or something sad. They were more likely to be miserable because they'd been torn away from their Christmas toys to do a boring shop.
If you have another adult in the family, leave them with the adult - either at home, cafe, park wherever.
Otherwise, online shopping is your friend.
As for sizing, I've nearly always bought my son's clothes without him being there. Never been a problem.
And:
How are they going to become independent adults if they have never set foot in a supermarket
because as they get older and more tolerant, you take them. Sigh. I've said this before, but some (most) chores really don't need practice. It's dead easy to go into a supermarket, find a basket/trolley, find what you need on a shelf and take it to the till (ok maybe the self-service till needs practice!). I think my ds will cope with supermarkets despite not spending every Saturday morning in one.
Why should it be one persons responsibility and why should you care
it can be shared between the parents (or doing online) and people care because screaming kids give you a headache. I feel very sorry for the staff who work in supermarkets.