Usb c has 24 pins. A typical barrel / stereo style jack has 2 - 4. The connector would have to be absolutely huge to carry the number of wires.
Power plugs are similar problems. You need 3 wires and you can’t risk the pins crossing over each other and shorting out. You don’t care about that on your headphones due to the low voltages. Wall plugs need to be fully isolated and safe.
It’s both ways. They effectively break that link and become isolated from each other.