Isn't there some way to just pad up the variable time that some sensitive operation takes, by spinning on a fine-grained clock register until it reaches a predetermined value? This could be calibrated by timing a known worst case.
Also, even if it were, one probably could detect that the CPU was just spinning from a side channel, for example by tracking CPU sleep state, cache line pressure or contention for integer units in the CPU.
(If we can track details like contention for integer units in the CPU, why don't we just peek at what bits are churning through the registers?)
Spinning until a fixed time is reached could conceivably leak information if another thread can time math-unit bandwidth; it would be able to distinguish the spinwait from bona-fide mathematical computation.
However, no (known) method accessible to code running on the machine can distinguish between an adder unit summing zeroes versus key data.
-> Can we just make sure the exact same operation operations occur?
On the other hand, as far as I know, looking at register content requires debugging rights, or would have to depend on a defect in the CPU.