It wouldn’t be that different from how a lot of cheese is being handled where I live. Except they currently put the cuts into plastic wrappings (which are “sealed” by the price sticker) instead of customer-provided containers. On the other hand, for fruits we already do use nets brought by the customer, and the weighing happens at the checkout.

In my hometown in Italy you can ask to put your cheese or cold cuts from the counter in a container you provide.

I'm not sure this ends up as a net positive compared to the paper with plastic lining they provide tho, since you have to wash the container at some point.