Over long distances the string will sag in the middle. That's one of the reasons (not the only reason) construction uses lasers today.

I have an asterisk in my post addressing that :) Happy to have picqued your mind.

BTW, your method was the method of choice for the surveyors of the Nile, from the Egyptian civilization.

Paper is hi-tech and was not available until much later, and as you mentioned doesn't scale. But if I have misplaced my ruler ...