I did that once. I wanted to go for a run, and I also wanted to buy some soup spoons from Ikea. So I ran to Ikea (about 4km away), and had to walk through the store all smelly and sweaty. It felt inconsiderate to the people around me. Then I ran home holding the spoons. Running while holding things is awkward. So there's two reasons. I haven't done that sort of thing since.
I do this sometimes, but usually for a few groceries. What I do is put a carrier bag in my pocket and do a gentle run to the shop so that I'm not too sweaty. Then walk home with the groceries in the carrier bag.
People already do that. But if you think a sizable proportion of the population will do that, you are mistaken.