I tend to agree. It's a very metagame situation to involve "resource balance" answers, and as such, it tends to deflate what could be a good, dramatic narrative.Right, I think if I was running 5e I might even just say to the fighter player "OK, you didn't bring a healer's kit, but if you pay some small cost (a libation, bleeding out an HD, something) you can basically have the benefit of one." That seems like an answer that would be pretty OK.
Honestly though, I feel like these simple "resource balance" answers, while they honor the concept of players needing to make resource decisions and build choices, don't extract maximum 'coolness' from the situation. I think this is a rather large lost opportunity and what separates ordinary play from really extraordinary play.
In other words, the above solution will work, and play will continue, and it will be little noted nor long remembered. OTOH if Death answers and bargains with the fighter and the consequences of the bargain shape his fate for the rest of the campaign to some degree, that feels like its falling more into the range of "wow, remember that time..." I mean, I've played a LOT of D&D, and I can tell you, there are only probably a few % of those games that I distinctly remember were super amazing.
That's why I wondered earlier if we as GMs could trust our players enough to carry the "consequences" of getting that favour completely on their own.