This passage therefore, may not have been put in the scriptures for the purpose of historical accuracy or dating, but to show Christ's genealogy (which would be pointed out in the New Testament). Thus would it not have been necessary to put ALL the fathers and sons in there? But rather put some so that his genealogy could be accurately traced/displayed?
Yes, it's not necessary to put all
the "fathers and sons" in, because the aim is simply to show that someone is a descendant of Jewish ancestry. Using your own example of your family tree which you have traced back to the 1300's, say for argument's sake that your ancestors in th 14th century were Danes, you would say that you are of Danish descent; however, it is taken as given that you 13th century ancestors were Danes- you haven't "proved" it by drawing up their own genealogical tree.