There's an additional key point that missing a single tooth-brushing does not cause cavities. If it did and:

- you knew when a person was out of toothpaste and going to the store to buy it

- you could implement differential for customers, singling out the customer(s) who have run out of toothpaste

- you could control pricing for all stores at which customers could buy toothpaste

Then yes, you could extract the full value of your toothbrush product.

Whether this makes it a platform would remain up for debate. I'd just call it a toothpaste monopoly.