The big problem is that Amazon has third party sellers and there is a strong incentive to use those third party sellers as a stepping stone to create their own brand. Since third party sellers are basically Amazon customers (they pay fees and use amazon services) Amazon ends up competing against its own customers. This is where the conflict of interest lies. Without third party sellers it's just another Walmart

House brands are not in competition with suppliers because house brands are often sourced from the same suppliers and labeling is actually a service that those suppliers offer.