Blockchains provide solutions to problems that require one (or more) of the following- 1)an immutable, transparent record of transactions 2) trust between parties that don't trust each other 3) optional anonymity 4) decentralization. Any one of these use cases could be a reason to use blockchain beyond the ICO use case.
It has a variety of use cases and so yes it would still be around. ICO's are a relatively new use for blockchains and it did fine before they appeared. It's usefulness for darknetmarkets was a primary feature in its initial adoption and gambling, well where you have money you will find gamblers.