In fact, even in the grocery retailing industry, there are integrations that would run afoul of the rule you are proposing. Kroger, for instance, sells brands it owns, while selling competing brands for what is, effectively, a commission. I'm not just picking on Kroger, all major chains engage in this practice. I was only using Kroger by way of illustration.
So what you're proposing has far reaching implications. I don't even think it's necessarily "bad", per se. But it does change the entire "order of battle", as it were, in the American retail space. Lots of people would go out of business, and lots more would be in serious financial trouble.