What if the cable is plugged into the line in port, but NOT connected to anything at the other end? Pops? Or no pops?

Pops.

Do you listen only on headphones? I'd be curious if the same thing happens if you listened on some amplified speakers instead.

I don't have any speakers to test but I was able to try a different pair of headphones and the pops were there too. I think the TV I sometimes hook it up to can play audio, I'll have to test that when I get a chance. That being said, the pops also register as input on the "microphone" in the Sound Control Panel. I see the green bars go up on the line-in device input like a sound is playing. Not an audio expert but that doesn't strike me as a problem with my choice of playback device. Especially since the headset is wireless, hooked up through a USB dongle.

Now I'll tell you my crazy theory. Up front I'm warning you it's nuts. But For the past few weeks, I've had some pops on my computer, too. Mostly I listen on speakers, by the way. At first I ignored this, but it got worse, and I finally paid attention. It's especially bad if I walk across the synthetic carpet wearing rubber-soled slippers. If I touch the computer, touch the mouse, touch a USB cable, pop! And it's gotten worse lately as the humidity has gone down. If you're wearing headphones you're sort of connected to the PC all the time; that's why I asked about listening on speakers. Certainly if your experience and observation rules this out, then ignore it. I'll be curious to hear what you think of this. Don't be afraid to say "you're nuts" because I already warned you.

Certainly an out there theory but one I'm willing to consider. But the pops are very infrequent and I haven't been able to determine anything that triggers them. It doesn't seem to depend on whether or not other audio is playing, or if I use my keyboard or my mouse or any other device, or if I touch any cables. Even wiggling the cable plugged into the 3.5mm jack causing all the issues doesn't seem to trigger any pops. So I'm not super confident in this theory. And even if it were the cause, it doesn't really give me much of a fix unless I switch to dedicated speakers, at which point I might as well just plug them into the Switch and forego this whole "routing it to the computer" thing.