Rav Eliyahu Dessler in Michtav M'Eliyahu (cheilek alef - p.8) has an essay that focuses on understanding G-d's trait of Rachamim - mercy, and in particular, how it manifests itself along with Zechus Avos.
He focuses on the specific middos that the avos excelled in and notes how it is this that creates a link to future generations. Their devotion and mesirus nefesh to the cause is what creates is our innate, ancestral link. For this reason one should read it not as 'zechus' but rather 'zakus' meaning the purity of the avos.
He writes on p.15:
הלא הבטיח השי"ת לאבות הקדושים כי תכלית כל הבריאה כולה תצא מהם וזרעם, וכל העתיד הגדול אשר יתגדל ויתקדש שמו של הקב"ה לעין כל, הלא יהיה על ידי משיח צדקינו. אבל הלא מאברהם אבינו ע"ה על דורו של משיח ישנן דורות הרבה, וכולם יוצאים אלו מאלו כמו השלשלת הארוכה, אשר טבעותיה דבוקות זו בזו. ובאופן כזה יש דורות או יחידים, שעל פי משפט מעשיהם אינם ראוים להתקיים, אבל מ"מ מתקיימים, לא בזכות עצמם אלא בזכות אבותיהם וצאצאיהם. כי הדור הזה, או האנשים הללו, המה כמו טבעת בשלשלת החבור ההיא, ובזה היא סבת קיומם, כי בלעדיהם אין חבור בין אבותיהם לדורות יבואו. אדם אשר כזה יתקיים בעולם הזה, אף שאין לו שום זכות לזה מצד עצמו
Did Hashem not promise to our holy forefathers that the purpose of all creation will come out of them and their seed, and all the great future which will grow and be sanctified in His name Hashem will be for all to see, and will it not be through Moshiach. But aren't there many generations from the point of Avraham avinu? All of them (i.e. the generations) come out of each other like a long chain whose rings are all linked with each other. And in this way there are generations or individuals, which according to the law of their deeds are not worthy of existence, but nevertheless they exist, not due to their own merits but the merits of their forefathers and their descendants. Because this generation, or these people, they are like rings in a chain that are interconnected, and this is the reason for their existence. Because without them, there would be no connection to the generations to come. A person like this will exist in this world, even though he has no right to it on his own part.
So to answer your question it would seem from Rav Dessler that this ancestral merit serves to aid our continued existence even when we are deemed unworthy. They showed us the correct way to act and these traits are something that we as a nation have been gifted throughout the generations.