Using fp-ts there is never a need for async/await and the code is still linear, (Promise is transformed to TaskEither<Error, Result>, similar to the example in the article, although you can ignore the error and just map over the result, handling the error somewhere near the end of the chain).
Problem with async/await is that the syntax is so easy that eventually the whole codebase gets polluted by it, even parts that could have been completely separated.
From the coding perspective, the problem with promises arise when there is a need to bind the intermediate results. You can either store them in an object and return that object for the next .then(fn) call, or you can nest inside a promise. I guess nesting is what annoys people the most (pyramid).