The first time we encounter Yerushalayim (Bereishis 14:18), it is under the rule of Malki-Tzedeq, a “kohein leKeil elyon — a priest of the most high G-d”, under the name “Shaleim”.
The other half of the city’s name begins with Avraham’s naming a nearby mountain, “har Hashem yir’eh — Mount ‘Hashem Will be Seen'”. Today it is called Moriah, the Temple Mount.
Notice that Yerushalayim was first the city of Shaleim, of wholeness (שלמות) and peace (shalom) and the city’s relationship to the Almighty follows.
And we find a related idea in a comment by Rabbeinu Yonah on the gemara (Berakhos 30a). The mishnah (on 28a) tells us to daven facing the Qodesh haQadashim. The gemara finds two verses to prove this, both by Shelomo haMelekh. The first is a quote of his prayer said at the inauguration of the First Beis haMiqdash, “וְהִתְפַּלְל֣וּ אֶל־ה’ דֶּ֤רֶךְ הָעִיר֙ אֲשֶׁ֣ר בָּחַ֣רְתָּ בָּ֔הּ וְהַבַּ֖יִת אֲשֶׁר־בָּנִ֥תִי לִשְׁמֶֽךָ׃ — and they pray to Hashem in the direction of the city which You have chosen, and of the House which I have built to Your name.”
For some reason, after expounding on this pasuq as a source for the law of facing Yerushalayim, the Beis haMiqdash and the Qodesh haQadashim when davening, the gemara asks for the source of the obligation in a pasuq:
אָמַר רַבִּי אָבִין, וְאִיתֵּימָא רַבִּי אֲבִינָא: מַאי קְרָאָה? ״כְּמִגְדַּל דָּוִיד צַוָּארֵךְ בָּנוּי לְתַלְפִּיּוֹת״ — תֵּל שֶׁכָּל פִּיּוֹת פּוֹנִים בּוֹ.
Rabbi Avin, and some say Rabbi Avina, said: What is its verse? “Your neck is like the Tower of David, built with turrets [talpiyyot]…” (Shir haShirim 4:4) — the hill [tel] toward which all mouths [piyyot] turn.
One might take this to mean that because we all follow Shelomo’s declaration to face the Miqdash when davening, as a consequence, all praying mouths will be turning to the same mountain.
But not Rabbeinu Yonah! He writes (20b, ad loc):
כדמפרש ואזיל כדי שימצאו כל ישראל מכוונין לבם למקום אחד
As it goes on to explain: so that all of Israel will aim their hearts to the same place.
Shelomo didn’t tell us all to face the maqom haMiqdash when praying because it is holy, a connection point to G-d.
Shalom and sheleimus come first, and only then it is the place where Hashem’s Presence is experienced. The Temple Mount is the holy place we face when davening because it was chosen to be the one place the Jewish People would be unified around when trying to connect to the Almighty.
(With thanks to Rav Menachem Zupnik for pointing out the implication of the one word “כדי” in that Rabbeinu Yonah.)