Note how concrete the rules are for chopping off a head, though: the player has an attack bonus, and a damage range; and the GM's notes tell him/her the AC of the creature, and how many hp the NPC/monster has; and the rules tell us that when the hp drop to zero, the creature is dead.Let's say you want to swing from a chandelier and chop somebody's head off. You don't have to ask the DM's permission to do this. You might have to ask the DM what skill & DC to use to do the swinging, and maybe because the chandelier is rather high, and the target is rather far off, he sets the DC higher than you would like, but I would hope the DM wouldn't just say "No, you can't do that." He (or she!) would say, "Ok, let's see either an Athletics or Acrobatics roll with DC 20."
As for the chopping off of the head, make an Attack roll. If you do enough damage to kill the target you should be free to narrate that as a clean head shot.
Now, your DM may choose to "not allow" either of those things. But if so, that's your DM, not the edition.
Now note how loose the rules for swinging on a chandelier are: there is nothing analogous to the AC, the hit points, or the damage roll. Knowing that I have (say) +6 to DEX (Acrobatics) tells me relatively little about whether or not I'll be able to perform the chandelier manoeuvre. Whereas knowing I have (say) +7 to hit with damage of 1d8+5, and can attack twice a round, tells me quite a bit about whether or not I'll be able to best a hoblgoblin in melee.
If the GM only sets the AC and hp of the creature after I declare my attack, then the difference between the two cases evaporates. That's why we get so many fudging threads, which - in the context of D&D - are focused almost entirely on combat. This combat/non-combat divide is an artefact of D&D, not of RPGing in general.
Even within the context of D&D, there is no reason why a character can't have an ability like "Dramatic Swing: if there is some appropriate furniture or similar about - a rope, a chandelier, a ladder, etc - then your PC can use it to move as normal without having to be on the ground. You regain this ability after a short rest, or by using an action to adjust/reposition the furniture in question." 4e PCs tended to have these sorts of abilities (especially rogue and ranger utility powers, and skill powers). In comparison, I think 5e PCs have fewer of them.