This is a very different problem than actual efficiency when mowing a lawn or vacuuming a rub. Turning takes more work and time, and you miss a part of the 'square' when you are turning (the arc of the curve is not a straight line). In addition, vacuums especially have an area at the edge of the machine that is not cleaned as well, which is why you want a bit of overlap in your lines. Plus, when mowing a lawn, you of…
Something like delivering newspapers would be a better problem I think - although I suppose you then you get into optimizations like preferring right-hand turns, etc. I wonder what would be the most simple and intuitive demonstration of the traveling salesman problem.