How will you use your supermarket to use Ethereum instead of their own blockchain where they can mine as much coins as they need without wasting huge amounts of energy?
If a supplier is running its own blockchain, then it really makes little sense. But to gain real trust of its clients, supplier will actually put it on a public blockchain. Only then external experts will say: "yeah, this supplier is really trustworthy". In other words, the incentive to use a public blockchain instead of their own, private one, is to gain real trust.