Is noise gating why you can't talk over each other? I am terrible at doing this (I think of it as synthesis - 2 excited ppl grabbing the idea, running with it, then the other interrupts and takes over) and while I acknowledge it's a bad behaviour, why do video calls or most digital audio ones not let it happen? I get there's delay so they can't exactly blend the two audio streams together, but what is this crazy limitation that only one person can talk at a time?
Delay/latency is a totally separate issue that also has negative effects but not in a way that I would characterize as intimacy. Full duplex vs half duplex plays into it as I alluded: the symptom of half duplex is that the louder person "wins" temporary exclusivity which causes the quieter source to drop out in a way that isn't entirely different from what a noise gate does; the difference is that dropping out due to half duplex is based on the relative levels of the two sources and dropping out due to a noise gate is based on the absolute level of the source being above some determined noise threshold. Either way, all the dropouts where quiet becomes silent result in a lack of breath noise, saliva noise, the kind of laugh that manifests as just a bit of a strong nasal exhale, and plenty of other sounds. Think ASMR videos.