If I may offer two big pieces of advice towards either adoption or truly making a statement that React might have to react to:
1. You probably need to answer the questions:
A. How do I use an existing React component? B. Can I use a component written in this inside of a React application?
If you can find a really good answer to either of these, and especially if you have a good answer for both, you can help get adoption. With as large as the overall React ecosystem is, it's going to be tough for any and all React-likes to gain traction without some sort of compatibility story. You don't have time for the React world to stop.
2. Testing. Probably the biggest contributor to the "components should be pure functions" orthodoxy in React comes from a well intentioned perspective of testability. Pure functions are indeed easy to test. It is easy to forget that they aren't always the only thing easy to test. I see you've got some tests for Crank.js itself in the GitHub repository, that's a great first step. I think you would make a stronger statement to the React orthodoxy if you added (and focused) documentation on testing each style of component.
I know from some experience there are some very good ways to test generators and even async generators. If you can show it and make it seem easy (because it should be), that could especially go a long way to saying why Suspense especially in trying to adhere to an early approach to keeping testing simple has in some ways pushed testing really complex.
So far as I can see the potentially most complicated part of testing will be how easily can you mock the `this` context. Should be something that is easy to build a reusable test context. Here too it should be possible to remind people that testing a custom function context should be as simple as `MyComponent.bind(testContext)` or `MyComponent.apply(testContext, {...props})`.
The more you can prove that testing all flavors of components here is simple to do, the more you might help assuage doubts that these aren't "pure" functions.