A good example of deferreds can be found in jQuery - every AJAX method returns a deferred that you can chain success, error, etc. handlers to. So it's not like this idea isn't a mainstream one.

The main problem I see is that very few libraries handle receiving promises as arguments, probably because there isn't a standard/widely-used implementation of them. So your logic ends up being backwards, e.g you'd chain Mustache.render off of a jQuery success promise, rather than just passing the success promise in.