why does quantisation noise sound like white noise?
It often doesn't sound like white noise. The quantization noise of a sine wave is fairly harmonic with a clearly detectable pitch. The quantization of a pulse train sounds like a pulse train.

If the quantization has enough bits, and if the signal is reasonably stationary in time and reasonably dense in the frequency domain, the quantization noise will be more or less white. For music quantized at 16 bits, that's often the case. However the quantization noise will always be correlated with the original signal which can produce undesirable artifacts. Hence commercial audio production uses dithering and noise shaping and decrease the audibility of quantization.