Still, the choice of glass is clearly cosmetic (less prone to scratch, nicer look, premium feel), buy technically plastic presents more advantages, it is lighter, absorbes shocks, fairly durable, much cheaper. To make for the most reliable device it would be better, but we know that’s not a priority for any of the manufacturers, and propably also for many customers.
You say the sound comes from the power supply and the HDD is not plugged into the computer. My diagnistic: the power-supply makes a noise when it operates at very low load (almost 0mA of current), it is probaly making the cyclic noise because of some blinking LED or another very small variation of the loaf somewhere. This is a very common symptom of cheap power-supplies, but it doesn’t necessarly mean it isn’t working normally, just an annoyance.
I suppose, when you plug the HDD to the computer, it spins up and start drawing more current from the power-supply and the noise disapears. This is because the PSU has a buck-converter, the switching frequency increase proportionally with the current drawn by the load. When the current it almost 0mA, the switching frequency can be audible (electromagnetic forces can make some components vibrate, e.g: coils). When the current is nominal, the frequency will be ultrasound and you won’t hear it. I have observed this with many electronic devices. If you are worried, you can try another power-supply, after checking it has the same voltage and polarity on the plug, and can deliver at least as much current as the original one.