I'm actually struggling to think of an example where I cared a lot about branching narrative choice in games (at least in the 'one big change' style of thing). For one thing, developers tend to put it at the very end of the game where making a choice doesn't actually result in any in-game change, but just changes the narrative coda a little. For another thing, by the time I've slogged there, I often care very little about what happens to the world afterwards - I'm not going to experience it, after all, so who gives a shit? See Human Revolution for instance, though of course they were somewhat hamstrung by being a prequel.
One alternative is making the player constantly choose options and then have a sum-up at the end of the game; the Fallout method. Mass Effect tried but the devs went nuts or something and instead of cumulative decision-making over the course of three games, well, we all know how that turned out. That's an alright way, though somewhat flat.
In terms of 'narrative' choice I've gotten a lot more into emergent systems-based choices with narrative flavouring a la Dwarf Fortress and other more systems-heavy games. But that's not really narrative in the same sense.
It's probably just unfeasible without a truly ridiculous amount of resources. Of course, that doesn't mean we should write it off as a failed experiment.