why does my USB 5V power supply not need a mains ground?
Wall warts although isolated from earth gnd, tend to have poor RF isolation and the switching frequency fields tend to be induced in the high impedance mic cables due to poor balance or CMRR, common mode rejection ratio.
There are several methods found effective to reduce this. Some are done in the SMPS with crossover RF caps to cancel the electromagnetic coupling of mains current.  Others are commonly done with high mu CM toroidal chokes molded on the mic cable. Others benefit from RF caps from 0V thru grounded interface cables to peripherals like analog monitors.
You can test yours with a Various caps to earth ground to determine where attenuation starts and thus compute the equal impedance half power point -3dB which is near the perception threshold for changes in power.(crude approx)
There are many more methods such as cable types , shielded balanced pair and differential amplifiers. The CMRR loss is usually in the cable type and shield or the use of multiple SMPS in a connected system so ground current paths are a concern. (Ground here just means 0V)
You can also try changing power to linear regulated supplies and keep away from strong SMPS stray fields.
I hope this gives you some ideas.