But the way ICOs work is you offer a token that people pay you for. If your token doesn't actually have any purpose whatsoever, then there's no reason for anyone to buy it.

Y'all are both right. Some tokens are (theoretically) required to use the app and some tokens will (theoretically) pay dividends like stock shares.

Tokens are more than that. They are not only fuel for apps (see: Ether), and "stock shares" that generate dividends (see the "stock split" of Bitcoin Cash and Bitcoin; see also Digital Developers Fund, Metal, and Etherroll, which has already PAID dividends to token-holders), tokens are also mechanisms for self-governance within an organization, required as a proof-of-stake to vote for the decisions the business is going to take (see DistrictOx0. Put more simply, tokens are a new asset class with the best of the old asset classes plus new, upgraded features from the new internet of blockchains.

For being on the y-combinator board some of y'all sure are slow seeing the gravity of the disruption.