Not necessarily impractical
The point isn’t the specific probe these researchers used to monitor the leak-path. It’s that data can be leaked at all from *physical attributes* of the cache. In other words, simply invalidating the cache (a known mitigation for timing attacks) does not wipe the potential leak-path, because that only zeros the valid-bit of the cache line, not the data itself. Reading the CPUs power management registers is only *one* way to acquire the data - the most obvious, but certainly not the best.The slowness of the attack is due to being able to read the power management API only every 1 millisecond. There are other physical probes that don’t have that limit.
Then it just becomes a game of finding some other apparently-benign physical sensor that is indirectly affected by power. For example: if the CPU power supply decoupling isn’t perfect, then maybe some LED intensity varies slightly with CPU load. Then the selfie-cam might pick up strobing in the video image. And now giving access to your camera may implicitly give access to encryption keys. There’s at least a dozen known variants of this sort of thing, if you know how to chain them.