As noted, USB headsets/speakers contain a ADC/DAC setup and act as new audio input/output devices. This is why plugging in a device may not register in a currently running app - it has already selected and connected to a particular device at startup. This is a Windows design issue, and not the fault of the app or the headset.
The USB headset configuration can be customised in hardware for a particular application (such as VOIP with echo cancellation etc). Also, the fact that USB devices can draw power from the bus means that the electronics can be more complex (active filters and gain/volume control, ALC or compression) as opposed to the passive controls of a simple earphone/mic setup. 3.5mm jacks are a broad brush interface with few defined standards for impedence, input/output levels etc. The output of a passive microphone may not be well matched to the mic input on a motherboard soundcard. A manufacturer will be much happier with a fully known signal path from audio to digital and back again. Finally, the ADC/DAC combination built into a motherboard is generally cheap, exposed to electrical noise and relies on system CPU, whereas with a USB device delivering digital data all the conversion is isolated and offboard. This gives manufacturers a higher level of confidence that that user will have a good experience.
If you have spent good money on a sound card for your computer, then it will probably be better (with an equivalent matched mic/headphone) than a USB based device. But for a simple motherboard based soundcard, the USB system will probably give better and more consistent results. But YMMV.