My maternal grandparents were born near Naples and my paternal ancestors immigrated to the United States from Sarnano, in the Marche region, near Ancona. So it is not surprising that my grandmothers' recipes for pasta sauce were meat-based tomato sauces.
You will note first that my sauce recipes do not call for fresh tomatoes. My grandmother (and later my mother and father) used tomatoes for their pasta sauce that they themselves canned each year – typically seven bushels of tomatoes each, or enough to last an entire year! They used a quart of canned whole tomatoes for each batch of sauce. Also, they all preferred sauce with no seeds – a preference I have acquired, or more likely, “inherited”. They used a conical strainer (what the French call a chinois) to remove the unwanted tomato seeds. (This was frequently my job!)
Needless to say, canning anything is not one of my favored activities. Commercially available canned tomatoes are perfectly acceptable substitutes, but removing the tomato seeds is still an issue (for me). Fortunately, tomato puree produces a superb sauce, every time, and with the least amount of effort.
In short, my decision to use puree instead of canned tomatoes is solely one of convenience. In fairness to my ancestors, however, I must add that their decision to use and strain canned tomatoes was one of economics, not efficiency.