For most PCs to survive a 20d6 fall would be 8-9+ level typically to average over 70 hp. When we talk about the extremely rare occurrences IRL of people who have fallen incredible distances and survived, how common are they? Then ask yourself, how common are PCs or whoever with 70+ hp? In my games, not common at all. So, for them to be one of those rare lucky individuals to survive such a fall is not a big deal really.
I agree with the others of course about the player metagaming it to a point, but if the barbarian has a history of making leaps and falling for any reason, maybe in character he just thought "I think I can make it." Smart? No. Possible? Sure.
Yes. In the case of the OP, I believe the behaviour of the character was more disruptive that the actual rules, not because it was wrong, but because it broke suspension of disbelief for that particular DM (and other players?).
But otherwise, IRL references are hard to translate in D&D, as stated before. I very much doubt that the person surviving the 1500 ft. fall kept on fighting or running afterward, let alone being conscious. They probably broke every single bone in their body and spent many months healing and learning to walk again. In D&D's terms, that's more like being reduced to 0hp, not dying outright, and succeeding on all three death saves.
That case, IRL, is a statistical anomaly. Not unlike rolling all 1s on 20d6 for 20 damage. For all we know, again translating into D&D logic, that person had 11hp, took 20 damage (just shy of being killed outright), had the PC "privilege" of rolling death saves, succeeding all three. In D&D, that's any 1st level PC with d8 HD and 16 Con, or any d10 HD with 12 CON, or a barbarian with 8 Con (or going
really meta, a raging barbarian with 3 Con). It's highly improbable, to the point of being negligible, but technically possible. In more likelyhood where the fall causes 70 damage, a 36hp character could survive, providing that all three death saves are succeeded. That's more like a 4-5 level character, or a 2nd level raging barbarian.