I don't do intense concurrency in the browser, but I'll do non trivial stuff, like collating responses from a server then sending a request once I have all that information. I think promises are fine for this and it is possible for most programmers to write clean, mostly mistake-free promise based code.
As for difficult to debug? I've never had that issue, neither in JS (browser/node) or C# with the similar but different Task<>.
For example in JS, I can put breakpoints at any point of the promise chain and see what is going on. If they are network requests I'll also look at the network tab. If everything is happening real fast I might use console.log statements, but that is rare.
I think promises are OK for a lot of situations that most of us will encounter developing business software - this might be a reflection on the simplicity of the problems I end up solving. Obviously if you are creating a multi-threaded high-frequency market making trading thing then this might not apply.
Might as well forget debugging in promise-land. I think this is partly because they are conceptually problematic as well, apparent once beyond the simplest use-cases, given the number of bloggers that still seek to explain it - and then are forced to edit their post because of errors. And the need to list common mistakes on MDN:
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guid...