I just find the whole idea of a 'narrative justification' for a character to be able to do the things they mechanically can do kind of trollish, since in practice it seems to only be applied to the mundane classes. (Not saying this is true of you personally, but it has been my experience)
No one asks the caster what makes them think they should be able to cast a spell to outrageous effect. They do it because they can, and the game moves on.
Yet the mundane class who can just do things because they're tough enough or skillful enough, or whatever gets to play the 'give the DM the right answer' puzzle game, and if they win, their class gets to function at full capacity, and if they lose, they have to go talk to the caster.
But then perhaps I'm just yelling at clouds.
I think that's a false comparison. Both the wizard and the cleric can attain sufficient HP to survive jumping off the cliff. However, I'm fairly certain that everyone here would not apply different consequences to them. They'd go splat right alongside the barbarian. As I said before, this is not a caster vs martial argument.
If the barbarian has a parachute, or got special training from an ancient warrior-sage and learned Meteor Fall (which allows him to ignore falling damage when intentionally falling) then the barbarian would be fine jumping off the cliff.
As I see it, this is an HP thing, and a genre convention thing, and a don't metagame thing.
HP (IMO) are not a force field. If they are a force field in your campaign, then I see no issue with barbarians jumping off cliffs. In my games, they are skill and luck. Skill isn't going to save you from free fall. Luck has limits.
Conan falls from many high places under many circumstances, but never because he simply thinks he's tough enough to take it. It reeks of bad fanfiction, and that's not the kind of tone I want in my game. It isn't something my players want to see either. It wrecks everyone's suspension of disbelief.
Lastly, I don't think characters should have a sufficient awareness of their HP, much less the falling rules, to be able to game the system this way. If they do have such an awareness, then they ought to be aware of plenty of other meta information as well. Level 1 characters should just go out and hunt 30 x CR 0 critters each. That's a much safer way to level up than actual adventuring, and the hop from level 1 to 2 is one of the biggest jumps in capability that characters ever get.
As far as I'm concerned, characters don't even know that HP exist, much less how many they have. A character with many HP would likely be confident, recognizing their own achievements, skills, and luck. They'd be aware as their own hp diminish that they're coming ever closer to losing. However, I disagree that they'd look at a 1500 ft fall and think, "I can take that". IMO, that's unabashed metagaming.
I'm not sure I 100% agree with
@Hriston 's scenario. However, I do agree with the idea of narrative justification. The player doesn't have all of the information. Just because they think the NPC is asleep doesn't mean they are. The NPC could be pretending. Or the PC might not roll well enough on their Stealth check and the NPC might wake up. The player doesn't know whether the NPC is unconscious and shouldn't simply assume that they get those benefits.
This impacts casters as well. Magic won't function in a dead magic zone, and it's unreliable in a wild magic zone, just to give two obvious examples.
To reiterate, I strongly disagree that this is a caster vs martial argument, as you seem to want to paint it.