That's not how the dying rules work. The DM isn't supposed to artificially invoke Instant Death, unless it's reasonably certain that the dying creature will receive no assistance. It's a fair call for monsters that you've just eradicated, but it's not a fair call for party members or pets.
That aura is a band-aid on the broken saving throw rules, where normal characters would otherwise fall off the bottom of the d20 roll. because making a DC 21 save would be impossible. It's not an elegant fix, by any means, but it's the only thing that keeps the promise of Bounded Accuracy alive.
Wisdom governs both Perception and Survival, which are the two most important aspects of exploration. I would say that a ranger contributes to exploration as well as a paladin contributes to socialization, except the ranger also has a lot of other class features that put them way out ahead. Rangers are amazing out of combat. It's possibly the one thing that they have, which puts them ahead of a fighter in any way.
Yes I found the Ranger was awesome outside of combat, which is why I think tweaks to the ranger should be conservative. Paladins are generally terrible at stealth.