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Did you know that people at the Scott-Amundsen South Pole Station have their own local ad-hoc'ish coordinate system for telling someone how to get from one building, telescope, or installation to another one? It's largely just a square'ish grid covering the whole area because things like "West" and "North" get a little squishy the closer you get to the pole itself. They're perfectly well-defined (outside of the pole itself) but trying to communicate the relationships between locations with them is headache-inducing and there's really no good reason why local navigation cannot just follow a grid that has been patched over the the usual lon/lat grid that just doesn't work very well at the south pole proper.
I am reminded of this every time I see people writing about black holes in (r,t) coordinates. Not that they're not perfectly well-defined (outside of the singularity itself) they just don't work very well to describe the relationships between events around an event horizon.