By "talking their way out of combat" do you mean the PCs persuading an initially hostile, even violently inclined, NPC/creature to be an ally or friend or otherwise to not fight?I think a thing that tables have a hard time pulling off is talking their way out of combat. BG3 does this to great effect, especially in act 2. I’ve never really seen it done otherwise. Thoughts?
If that's what you mean, it's something that happens reasonably often in my RPGing. In 4e D&D this would be resolved as a skill challenge; here's an example:
When the Tower shifted into the Feywild the PCs (following the hag's directions) headed north. The invoker summoned them phantom steeds, in the form of giant flying dragonflies. (When the player mentioned the dragonflies, I suggested rainbow gossamer wings, but he wouldn't come at that. So the Feywild charged him 100 gp rather than 70 gp worth of residuum for the ritual.)
As the PCs were flying along, they saw an eladrin hunting party, with a displacer beast pack, below them in the woods. As they were turning about to investigate more closely, the eladrin feyknight whistled and called the drow sorcerer's dragonfly to him. (The mysterious magic of the Feywild!) Pleasantries, which included the drow prominently displaying his symbol of Corellon to prove his good faith (he is a member of a small drow cult of Corellon worshippers who seek to end the influence of Lolth and undo the sundering of the elves), revealed that the eladrin was a Marcher Baron, Lord Distan. (The PCs and players recognised that name, as someone who had kicked the hags out of their former home 20-odd years ago, leading them to taking up residence in their Tower instead.)
He invited them back to his home, where it quickly became clear that he didn't really want their company, but rather wanted them to help him with a problem - he was expecting a visit in a few days from his Duke overlord, but his special apple grove was not fruiting as it normally would.
This was an adaptation to 4e mechanics and backstory of the scenario "The Demon of the Red Grove" in Robin Laws's HeroWars Narrator's Book. The reason for the trees in the grove not fruiting is that a demon, long bound there, has recently been awoken but remains trapped within the grove, and hence is cursing the trees. Mechanically, this was resolved as a skill challenge. First the PCs had to endure the demon's three cries of "Go Away!" (group checks, with failing PCs taking psychic damage - the sorcerer, who is also a multi-class bard, was the most flamboyant here, spending his Rhythm of Disorientation encounter power to open up the use of Diplomacy for the check, which in the fiction was him singing a song of apples blossoming in the summer). Somewhere during this process the cleric-ranger and invoker both succeeded at Perception checks and could hear the high-pitched whistling of a song bird. And the sorcerer's Arcana check revealed the presence of the demon - an ancient and mighty glabrezu (level 27 solo, as I told the players in order to try to convey the requisite sense of gravity).
At this point I thought they would attack the demon, but they decided to speak to it first, to find out how it had got there and what it was doing there. With successful Diplomacy checks they learned that it had been summoned long ago during the Dawn War ("When Miska's armies were marshalling on the Plain of a Thousand Portals") by a powerful drow who had come into the Abyss, in order to ambush a strong and cruel sorceress. But the sorceress had defeated it and trapped it in the grove. When they asked it the name of the sorceress, it replied that the name had been erased from its memory - at which point the player of the paladin of the Raven Queen worked out the sorceress was his mistress, and the player of the drow worked out that the ambusher must be Lolth. They also learned that it had been woken a year ago by an NPC wizard who was, earlier in the campaign, a nemesis of the PCs, as part of his attempts to learn the true name of the Raven Queen.
They then debated whether to bargain with it, but doubted its promise that "My word is my bond." The player of the invoker decided to use the Adjure ritual - that works on immortal creatures only, so he used it to try and change the immortal magic of the Raven Queen that was binding the demon. Instead of being trapped in the grove, they wanted the demon to instead go forth and fight frost giants and formorians. A roll was made (with help from the paladin, the ranger-cleric (who is also a Raven Queen devotee) and the sorcerer (who hates the giants because they serve evil primordials and he serves Chan, a "good" archomental). Unfortunately the roll was not very high, which meant that even with the bonuses it didn't achieve a full success, so the demon is bound for a week only - and hence was quite cheerful as it flew off to the north to beat up on frost giants.