Generally I'm in favor of seeing hit points as mostly fatigue, but the rules created mix actually works pretty well when you step back. All the corner cases people talk about (poison, shouting somebody up from unconscious...), require a person to be attached to a very specific idea of what the exact wound is for it to be an issue.
But if you just let things be a mix, with the idea that if the PC is still standing, it was a very minor injury, it works great. Getting hit by an arrow isn't 8 points of actual body damage, it's an arrow that barely penetrated the armor, leaving a little blood and some pain, but not something you would ever have to see a doctor for. The same sort of injuries boxers, football players, & wrestlers sustain all the time, and shake off without a hitch. Essentially, the same sort of injury that would have no effect on your strength or speed, and your warlord friend could just inspire you to ignore so the lost hp go away even if you still have a small cut somewhere.
For instance, imagine a high school football game. All those players have hp, over the course of the game, some of them are drained. Most of it is just fatigue, pain, and bruises, so they don't go down to 0 hp. But every once in a while, a player crits on another player, and takes him out of the game at least momentarily. That player went below 0 hp.
Sometimes the player just needs a moment or two to rest (second wind) or a pep talk from the coach (inspiring word) and he can get back up. Sometimes it's more serious (necessitating prolonged recovery). While D&D doesn't have any specific rules for long term injuries, the closest analogue would be PC death (out of the game in both examples). Since the game doesn't model long term injuries with penalties, just play HP as a mix leaning heavily toward fatigue until the PC is below 0 hp. That's the spot where you can play up or down how much actual physical damage you want a PC to have (house rule a long term injury, narratively decide what losing means, or have the PC die of a fatal final wound). Since the official rules still don't specify what exactly that final blow is, you're still free to find an explanation that fits the in-game actions best. Really, the only thing you need to do is describe less than 0 hp as incapacitated instead of unconscious, so you don't have people complaining that the warlord just shouted somebody awake from unconsciousness (even if it is realistic, and I have personally done exactly that many time in the back of an ambulance)
tldr; a mix of fatigue, skill, luck, and actual injury works great if you weight it towards fatigue and only allow injuries that are minor enough to have no impact on you stats (strength, speed...). If you wound is so minor you aren't slowed by it, you can have a warlord tell you to ignore it even if it was large enough to administer a poison or whatever. So leave it a mix for simplicity sake, and make what happens at below 0 hp where you start to tweak things.
Edit: I almost forgot, by making the blow that brings you below HP that one that matters, it also allows you to set the penalty for being below hp according to the importance of the target. Monster suffer a fatal blow because they aren't important, a PC might suffer a long term injury or be knocked unconscious and captured, so you don't have to due to raise dead/resurrect shuffle. It's flexible enough to let each table twist it to suit the story, and makes the penalty for running out of hp clear (you lose or whatever that means in the current situation).