A screw cutting lathe requires a good lead screw as its reference. Maudslay invented a "screw origination machine"[1], a clever special-purpose device for making a more accurate screw than the one you have. It only cuts soft metal, so the screw it makes is used in a second lathe to make one in hard steel. This is another of the key steps in bootstrapping to precision.
Early precision work was limited to flat things and round things. Take a look at a steam locomotive from around 1900. Every surface that has to be held to a tight tolerance is flat or round. That's because the precision tools of the era were the planer, lathe, and drill. The general purpose milling machine came later.
Incidentally, this is the real reason manholes were round. In the great era of city sewer-building, you could make round metal manhole covers easily, by casting and a quick lathe pass. The ring into which they fit could also be easily finished on a lathe. Making an iron rectangular frame and a lid to fit it would have been a much harder and more expensive job.