So it would be a platform if you had a dominant company whose brushes would require certain kinds of pastes. Since most toothbrushes are completely interchangable as are pastes created by those same companies, there's nobody really building their business on top of any of those particular "platforms".
- 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.
You're mistaken about what Gates meant by "economic value".