It makes sense that המקום אשר יבחר ה׳ would be based on the historical connection of the אבות to the land. But there really are five different choices:
So if I am in charge of finding לשכנו תדרשו ובאת שמה and I want it to connect to the historical centers of עבודת ה׳, I have five choices: שכם (also called אלון מורה), בית אל (also called לוז), חברון (also called אלני ממרא, not to be confused with אלון מורה), הר המוריה (also called שלם and ירושלים), and באר שבע. Two of them are associated with two אבות: שכם and בית אל.
And one of those is explicitly mentioned in the Torah; in fact, in our parsha, the very paragraph that talks about המקום אשר יבחר ה׳ starts with a very detailed description of a place:
And this ברכה/קללה ceremony is described in greater detail in פרשת כי תבוא:
So what’s the question? The central מזבח and the בית המקדש is to be built in שכם. It is the geographic center of ארץ ישראל; it is at the crossroads of the major north-south and east-west trade routes (the 60 and the 57 today); it the first city you come to when entering the land from the north (see Avraham and Yaakov’s journeys). The Samaritans obviously are right.
When the people come into the land, they have the ceremony in שכם:
And Yehoshua actually moves the ארון there for a re-enactment of the ברית:
So the מקדש actually is in שכם. But it doesn’t stay there; it goes to שילה (and then to ירושלים). And there is subtle textual hint that the מקדש belongs in שכם. The first place we see a כהן to G-d is in שלם, which we know is Jerusalem:
But is it really? Remember, ויבא יעקב שלם עיר שכם אשר בארץ כנען בבאו מפדן ארם:
So Shechem had at least the potential to be the spiritual center of Israel.
And it could have been the political center as well. We don’t remember this, but there was a king of Israel before Shaul, and his capital was not Jerusalem but Shechem:
He wasn’t a good king. He slaughtered his 70 brothers (as kings are wont to do), and was eventually assassinated by his own people. And no one wanted a king for another 160 years.
Shechem has a history as the center of the country, but it’s not a good history:
And it goes back to the first time the tribes fought each other:
And that is why the בית המקדש cannot be in שכם. From the times of Avraham and Yaakov, it had the right history to be the resting place for the שכינה. But when the brothers sold Yosef, it became the symbol of the שנאת חינם that would tear the people apart.
The place of the בית המקדש can’t just be a place for עבודת ה׳; that is only half the Torah. It has to symbolize a place where וישבתם בטח, where everyone can live in peace. As we discussed on this parsha three years ago, the purpose of the ceremony at שכם was to achieve closure and then move on from the פרענות of מכירת יוסף.
That’s why the בית המקדש is built in Jerusalem. Of all the cities in ארץ ישראל, Jerusalem until the time of David did not belong to any of the tribes; it literally belonged to all of the tribes equally.
המקום אשר יבחר ה׳ has to be עיר שלם, both למען בית ה׳ אלקינו and also למען אחי ורעי.