It's been a long time since I was a land surveyor (total stations were just taking over the theodolite and tape, and GPS was a mere pipedream) so much is lost in the mists of time, but the reason I didn't deal directly with the earth's curvature was because I was surveying in relatively small distances (~500m (curvature ~0.02m)) and the results were mapped onto a map projection that already takes care of the curvature (as far as we were concerned anyway). Had I been involved in large scale surveying (ocean oil pipelines, etc) or across different map projections I would have had to take more care about the curve.
If the earth was flat, we wouldn't need the 000's of different map projections.
If I plot a straight line across the Atlantic using a Mercator projection, I could follow the line and sail to the point I'd selected (if I could sail a ship at all, that is). But if I measured the lands at different latitudes, that were the same size in the map, I'd find a huge difference between them on the land.
But if I took an equal area projection, Gall_Peters for example, I'd find the equally sized lands at different latitudes were equally sized on the land. But trying to follow a straight line to navigate from the map I would end up miles away from my destination.
These discrepancies are because of trying to flatten a spheroid. If the world was flat, it would be impossible to come up with a map that was able to provide accurate lines of true bearing in all directions, and incorrect areas.