There is no "partially" supported. An USB audio device typically supports a limited number of sample rates, channels and bit depths. Usually, that is only one: 44.1 kHz, 16-bits, 2 channels or maybe 48 kHz, 16-bits, 2 channels. Especially the cheapo ones.
The USB audio drivers are always able to convert about any WAV input file in practical use to that target format. If that does not work, you have likely not fully installed the USB audio drivers (including additional components that they update).
Look at the WAV file you have problems with. What sample rate, bit depth, num channels does it have ?