An article on the OU website here answers this question.
As a starting point, one needs to look in Zechariah where the construction of the Second Beis Hamikdash is underway. The question posed at the time was whether there should still be a chiyuv to fast on Tisha B'Av if a new Temple was being made (Zechariah 7:1-3).
Zechariah goes on to relate Hashem's response (7:4-6):
וַיְהִ֛י דְּבַר־יְהוָ֥ה צְבָא֖וֹת אֵלַ֥י לֵאמֹֽר׃ אֱמֹר֙ אֶל־כָּל־עַ֣ם הָאָ֔רֶץ וְאֶל־הַכֹּהֲנִ֖ים לֵאמֹ֑ר כִּֽי־צַמְתֶּ֨ם וְסָפ֜וֹד בַּחֲמִישִׁ֣י וּבַשְּׁבִיעִ֗י וְזֶה֙ שִׁבְעִ֣ים שָׁנָ֔ה הֲצ֥וֹם צַמְתֻּ֖נִי אָֽנִי׃ וְכִ֥י תֹאכְל֖וּ וְכִ֣י תִשְׁתּ֑וּ הֲל֤וֹא אַתֶּם֙ הָאֹ֣כְלִ֔ים וְאַתֶּ֖ם הַשֹּׁתִֽים׃
“[And God said to me:] Say to the people…When you fasted and lamented on the fifth and seventh months [i.e. Tisha b’Av and Tzom Gedalya] during the last seventy years, have I been fasting?! And when you eat and drink (not on a fast day), is it not you who decides to eat or drink?!”
The OU website writes:
Note how God’s rhetorical answer implies that Am Yisrael should not be asking God concerning the laws of the fast days. After all, the fast days are not God’s commands, rather they are customs instituted by the people themselves in order to remember Yerushalayim. Just as the people decide when and what they eat, they too should decide if and when they should fast....
...God takes this opportunity to remind Bnei Yisrael (7:7-10) that the first Temple was destroyed because of their wayward behavior, for they did not follow the guidance of their prophets. To make sure the new Temple will be successful, the people must make sure not to repeat those same sins that caused the first one to be destroyed.
In a nutshell, God is not interested in people fasting; rather that they follow His laws properly, especially those of social justice, and not repeat the sins of their forefathers.
Thus, after making it clear what His aspirations are for His people i.e. to follow the way of truth and justice, all four fast days are addressed Zechariah 8:18-19
וַיְהִ֛י דְּבַר־יְהוָ֥ה צְבָא֖וֹת אֵלַ֥י לֵאמֹֽר׃ כֹּֽה־אָמַ֞ר יְהוָ֣ה צְבָא֗וֹת צ֣וֹם הָרְבִיעִ֡י וְצ֣וֹם הַחֲמִישִׁי֩ וְצ֨וֹם הַשְּׁבִיעִ֜י וְצ֣וֹם הָעֲשִׂירִ֗י יִהְיֶ֤ה לְבֵית־יְהוּדָה֙ לְשָׂשׂ֣וֹן וּלְשִׂמְחָ֔ה וּֽלְמֹעֲדִ֖ים טוֹבִ֑ים וְהָאֱמֶ֥ת וְהַשָּׁל֖וֹם אֱהָֽבוּ׃
“Thus says the Lord: The fast of the fourth month (17th Tammuz), the fast of the fifth month (Tisha B’av), the fast of the seventh month (Tzom Gedalya), and the fast of the tenth month (10th of Teves), shall become for the House of Judah days of joy and gladness – happy festivals – [on the condition that] you must love and follow – emes v’shalom – truth and peace. ”
And as a result:
God declares that should Am Yisrael fulfill their destiny and establish a nation characterized by justice & truth, there will no longer be any reason to fast. Instead, these fast days will become holidays.
So it would seem from this analysis that all of these fast days were characterised by failings in the Jewish people, particularly in the area of social justice. When we as a nation take pains to correct these flaws all of these four fast fast days will be celebrated as holidays and that is why so many of our fast days "revolve around the Beis Hamikdash".