The picture and dongle shown are worth the scorn the internet has given them. That said, this is their "solution" for someone who wants voice chat AND game audio in their headsets at once, right? Hori is basically trying to fix what's broken in Nintendo's online chat solution.
I don't know, ladies & gentlemen, I can't say I'm surprised it's come to this when everything ABOUT the Switch is in effort to make compromises. I do wonder if Nintendo worried that voice chat internally on the Switch would add extra burden for a console that would already seem underpowered at launch compared to its competitors. Limiting the system features on-board is one way I suspect they're able to ensure as much of the processing power is available for themselves and Devs to devote entirely to how the game runs.
That said, as an example, when I play overwatch on PC, I actually have the sound route through the desk speakers and have one hear on my headset. This works pretty well and helps me better hear teammates. I also have an old iphone I haven't tried to sell yet exactly for this purpose, so it's not going to take up my phone availability anyway.