No ATC doesn't routinely give this sort of instruction, though of course lots of the "legacy" fixes were and still are defined as a radial/DME. I think the last time I saw the method being used even slightly in anger ( to cross check a questionable ATC instruction) was on the Classic 747 over darkest Africa. So pre-glass screen, pre a GPS fit....as you say these days it doesn't work like that.
Certainly when I taught it (in a non civvie environment) we knew even then most students would never use the technique "in anger" but the logic for teaching it was pretty much as backpacker described earlier:
I think your FI is not doing this to prepare you for real life. This is just an exercise to see if you can think on your feet, and can visualise what's going on.
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It certainly was a good instructors tool for seeing how full a student's capacity bucket might be getting....now whether that is relevant in a civilian teaching environment in this day and age is another matter, maybe they should just teach how draw and follow a magenta line.