Not noise, more specifically current loading.
I jumped a step or two in my reasoning. More current loading makes for more signal-dependent noise on the power supplies (due to circuits not operating in SE classA). The greater the noise on the PSU the more gets into the signal at the output. So more noise is a direct function of additional current demand.
SMPS supplies with fairly high carriers and residuals tend to cause the "etched" sound we know to be familiar. But many manufacturers using them have effectively reduced them down to very low levels. I get no trace of it, say, from an MSB DAC.
Its possible to tame switching supplies' noise. Just that there's no incentive to do that (filters are expensive to add) when the supply's intended for some purely digital piece of kit like a PC.