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Side-channel attacks are an inherent property of computing hardware. You can never fully "disguise" a computation as a different one or as no computation.

You can just lower the signal to noise ratio by various means, so you gain some time until better statistical methods or clever tricks filter out the signal again.

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There are side channels and there are side channels. A computer fan outputting noise is a side channel that indicates both that a computer is running and may indicate something about the workload, but if you are close enough to hear it, you are close enough to do a lot more than listen to the fan noise so there is no real more in suppressing it.

Isolated processes being able to determine the memory or computation of another process is something else altogether and surley could be mitigated, even if the mitigation comes at a cost.

You can have the fan on fixed rpms, hence the only side channel is that the machine has power.

But that would be wasteful and needlessly noisy. The point was that there is no need.

There's more. Vibration and electromagnetic emissions (TEMPEST) are also viable side channels. Or ultrasound in speakers to cross airgaps.

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