Sound, as it travels through the air, is analog. To convert to and from analog to digital, you need a D/A converter, power, and for output, an amplifier. So it's a logistics problem: where do you put the converter and circuitry, and why? And how do you get power to it? (More importantly, how do you get power to it without mangling the audio signal?)
Headphones use analog connections, usually, for cost reasons. Cheap ones are cheap, and cheaper is better. Conversely, manufacturers of expensive headphones are assuming that you will be plugging them into a much nicer D/A converter and amplifier than they could possible build into the headphones themselves. But the cables are, presumably, verity high quality, and if you're an audio nerd, you're going to be smart enough not to wrap the wire around a power strip or something, so interference shouldn't be an issue.
In the middle ground, there are USB headphones.
Microphones are basically the same story. Cheap ones are cheap and don't have D/A converters because cheap. Expensive ones are expensive and don't need D/A converters because you already have an expensive D/A converter, and there are USB microphones in the middle.
There have been a few different digital connection standards over the years, some were brand-specific. I haven't seen any coax in a while - most of my digital stereo gear used S/PDIF. (5mm square connectors.) And many motherboards have S/PDIF outputs. A lot of newer computers use 3.5mm optical out because you can do a dual-mode optical/analog on a single port. (This used to be standard on Apple computers, dunno if it still is.)
In the last ten years or so, devices that were intended to interface only with computers have usually had USB interfaces. (Headsets, speakers, audio interfaces, microphones, etc.)