If the rule only affected online house brands, it would tilt the field in favor of Walmart, Costco, and Kroger, who could all continue selling their house brands in stores. For e.g. Kroger, where online sales are a tiny percentage, this would essentially represent a carve-out.
Looked at another way, this could be seen as a tax on people with mobility challenges. (Because no house brands on the delivery services => higher costs.)