There’s nothing saying you can’t “roll for initiative” in a cut-throat round of verbal sparring, in particular with an audience in a face-saving/reputation-driven culture where insults would do more lasting harm than a physical scar would.
Part of the challenge is that while most RPGs have intricate rules for dancing through combat that we’d never deign to emulate in real life, most GMs/players choose to act out the verbal interplay and non-combat actions in the most literal of senses.
Look, I can’t swing a sword worth a shit in real life — I know, I’ve tried. That doesn’t stop me from playing one on the tabletop, and living vicariously through that character sheet.
However, I’m not a half-bad wordsmith, particularly when given a chance to prepare some remarks in advance, and so there’s some non-combat interactions that I can act out in literal fashion.
What doesn’t exist in a particularly well-defined way in any game I’ve played (and I started on RPG’s in ’81) is a good set of compelling, interactive, and urgent rules for non-combat interactions that generated the same pulse-pumping feel that combat does (particularly with a GM that uses a timer for combat so you have less time for ‘planning’ during the battle).
So while I can’t swing a sword, I can act out a bard or a diplomat or a glib merchant. But my less-verbally-gifted friends? There’s no good set of rules that lets them vicariously engage in non-combat actions the same way we all get to do so once the swords start to fly, and that severely handicaps the less-articulate players around the table. Similarly, the sense of urgency based on what one GM friend called the “Relative Likelihood of Imminent Demise” makes non-combat encounters feel like filler from their lack of lethality, but if you can instead weight them in such a way that ‘losing’ a non-combat encounter would force the players to leave town, or severely inhibit their next encounter, or end their employment/quest, then there are real stakes at play and the urgency is back.