They do, the two supermarkets in question photograph the product provided for sale and show labels which manufacturers are required to have on their products. They don’t have any legal requirement to do such, but have chosen to do so.
We are talking about 2 different businesses. The first being those which manufacturers food products, but doesn’t retail them. They don’t sell online but may or may not have an online presence. These businesses are responsible for the products they make, including meeting statutory, labelling or stewardship requirements.
The second being those who don’t manufacture food products, but retail food products manufactured by others. Some buy direct from the manufacturer, others through wholesalers or distributors. These businesses may sell online. These businesses have different statutory requirements and aren’t responsible for product labelling.
What is being proposed is the second business being responsible for part of the statutory, labelling or stewardship requirements of the first, for which they have never had in the past responsibility for.
It doesn’t change consumer rights. Consumers can readily obtain the information from product photos. The two supermarkets singled out for criticism provide these photographs. Many don’t.
What is being suggested potentially causes or substantially increases the risk of consumers being provided with incorrect, out of date or information inconsistent with product labelling. This is because it sets up a secondary system attempting to duplicate product labels information directly in retailers webcontent. It also transfers some of the responsibility of that of the manufacturer to the retailer, when the retailer has no control and in the past, no legal responsibility for the information (with exception of food manufacture/preparation at the retailers premises).
I have seen in the past where a government has tried to broaden responsibilities for one business, to other businesses which aren’t in control of the issue at hand. It quickly became a train wreck as businesses quickly absconded their responsibilities in attempt to push it onto others. It doesn’t work and like this, would be set up for failure. Such is also not in the interests of the consumer.
Edit: An example of failure is when a manufacturer changes processing to remove a known allergen risk from a product. The retailer updates their website, but still is likely to have products in stock with the allergen risk. If a consumer buys the product based on webcontent information, who is responsible if they are injured or die from incorrect information. One could say that the retailer could wait until all the product is sold… but what happens if the newer product has a new allergen. What happens if they delay posting this allergen and someone gets injured or dies. Who is responsible? This shows a major possible failing of what is proposed and not in the interests of any consumer. One might argue the risk if this scenario is low - however many store branded (and branded) products change frequently to meet the consumer/retailer appetite for cost efficient products. All it would take is for one injury or death to have a secondary/duplication system fall over. This is where consumers should possibly only rely on product labels attached to the product in hand. Any other sources might be interesting, but should be considered unreliable. These timing mismatches don’t exist with product labels.