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So, remembering the exact location once, and then tracking all movement with almost absolute precision, thus calculating all future locations? Did I get it right?

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Basically yes. If you want to get technical about it, it's not tracking movement it's tracking acceleration, which you can then integrate twice to update position.

Technically, acceleration is movement in an inertial system... Anyway, I was wondering for a long time, why phones/watched don't attempt to do it (at least, I never saw useful results of it). Surely it would be more useful to me than nothing, when lost in a labyrinth underground. I always assumed, that results are so horrible (close to random) that nobody even bothers. But then it doesn't tell me much if there is an accelerometer 1000 or 1M times more accurate, in a shoe-box or otherwise. Like, how often does it have to re-calibrate after all?

Are there any records of how currently available consumer devices measure up in this regard?

After integrating the output twice from current COTS accelerometers, position is useless in at most a few minutes.

You might be interested in this app to try it for yourself:

https://github.com/nisargnp/DeadReckoning

I read a paper some time ago which suggested that mobile devices are still nowhere near good enough to use this e.g. for navigation around a shopping mall.

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