I'm totally on board with futures, IF your application needs to scale to the point that blocking, threaded computation is infeasible. However, I honestly don't think that's the case for most folk. Blocking, direct-call computation is way simpler than futures.
Fibers are fine as an idea. But all the C++ implementations I'm aware of require the programmer to mark up their code for cooperative scheduling. That's a non-starter for me.
They are intrusive in the sense that the code looks much different. On the other hand, I'd guess they are less error prone. Marking up syscalls would be a constant cognitive load, since you have to remember to do it each time (or else maintain an abstraction layer). But once you've decided to use futures, that's just how you do async.
I think the language and framework are also important in deciding to use them or now. In modern C# with MVC/WebAPI it feels wrong to me to NOT use async/await/Task (the .Net version of Futures and Promises). For fairly little change in coding style you can get some big performance wins on IO code.