But in a game, 'defeat' - real defeat - I think needs to be an option on the table. I've seen 'fail forward' defined in ways that argue for failure to be succeeding at a cost, such that real failure is removed as an option.
I am not sure the fact that someone, somewhere, argues for something extreme, really is a basis for something we should worry about.
As a counter to that argument, let us look at actual implementations. I expect the most commonly used version of "succeed at cost" is probably found in FATE. And in that game, the implementation is that there are several levels of success, which we can usually paraphrase as failure, succeed at cost, success, and great success. Basically, the things that in other games are considered just barely failures, in FATE, tend to become "succeed at cost". Outright failure is actually still a possibility.
So, really, all you who are griping about failure being on the table - it usually still is. Don't get in a twist over it.
But in a game, 'defeat' - real defeat - I think needs to be an option on the table.
Note that "fail forward" is typically applied to *individual actions* - in most game terms, single die rolls. It does not generally apply to overall efforts. We are talking about having a way to progress in the middle of the story, not a way to ensure success at the end.
In my opinion, you can't really savor a character surviving if death never really was a meaningful possibility.
To continue my example, the Success at cost mechanic there will not save you from death. In most FATE variants, the mechanics take you to the point of being "taken out" and "success at cost" can't forestall that forever. At that point the character's continued existence (PC or NPC) is up to the person who took them out of the fight. If you want 'em dead, they're dead. If you want to incapacitate them, you incapacitate them.