There's an interesting dilemma here you're not considering. Any more red tape here would make it extremely difficult for legitimate small businesses to sell anything online.
Simple solutions that you have just thought about usually don't work, especially when the topic seems like it might employ several researchers and lawmakers.
If your business is to source from all 6-letter random “IOWURP Products”, then quality checks becomes your job. Unhappy? Then do like all other distributors: Only accept direct deliveries from Sony and Beats.
That there may be some regulatory capture where the fines don’t really matter, but we have a system in place to deal with fraud and unsafe poor products.
Amazon/Temu etc would just prove legally that they are not the ones selling the product.