I do bring in a pannier or 2 into the store with purchases from a prior store --after all, I keep my wallet, keys in there. And the bags are like people's tote bags, etc. I do hope the stores I visit have shopping carts or wheelie baskets so that I can throw in my panniers into the shopping cart to relieve myself of weight.

Occasionally I leave a pannier still hooked onto locked bike outside. If I have to leave something in there, it would be food. Nothing else. Not even gloves.

Carrying around 1 pannier in store, is like carrying around a large handbag or tote bag --like many women.

I've never had problems with security/the stores and have been cycling-shopping like this for last 2 decades in all the cities I've lived.