I think the most appropriate way to begin this discussion is to start off by discussing the genesis of this holiday. In Shemos (12:12-13):
There are many other places in the Torah where the Jews seem to have a mass repentance and then, only once they return to religious observance, do they celebrate the holiday of Passover. The first occurrence of the Jewish people keeping Passover outside of the first five books is found in Joshua (5:2,6-8,10):
|ב בָּעֵת הַהִיא, אָמַר יְהוָה אֶל-יְהוֹשֻׁעַ, עֲשֵׂה לְךָ, חַרְבוֹת צֻרִים; וְשׁוּב מֹל אֶת-בְּנֵי-יִשְׂרָאֵל, שֵׁנִית.||2 At that time the LORD said unto Joshua: 'Make thee knives of flint, and circumcise again the children of Israel the second time.'|
|י וַיַּחֲנוּ בְנֵי-יִשְׂרָאֵל, בַּגִּלְגָּל; וַיַּעֲשׂוּ אֶת-הַפֶּסַח בְּאַרְבָּעָה עָשָׂר יוֹם לַחֹדֶשׁ, בָּעֶרֶב--בְּעַרְבוֹת יְרִיחוֹ.||10 And the children of Israel encamped in Gilgal; and they kept the passover on the fourteenth day of the month at evening in the plains of Jericho.|
It was only once the Jewish people had a mass circumcision and the generation that had the Sin of the Golden Calf and the Sin of the Spies, that caused the Jews to wander in the desert for 40 years, passed away did the Jewish people once again keep the Passover.
The Kind Hezekiah is found to be a completely righteous king, but he followed a completely wicked king. Therefore, when Hezekiah inherited the kingdom, his subjects were idol worshipers. This can be seen in Chronicles 2 (29:6,7):
After King Hezekiah had the Levites cleanse the temple and he destroyed all of the idol worship, he moved on to congregated everyone in Jerusalem to celebrate the Passover holiday (Chronicles 2 30:1):
|א וַיִּשְׁלַח יְחִזְקִיָּהוּ עַל-כָּל-יִשְׂרָאֵל וִיהוּדָה, וְגַם-אִגְּרוֹת כָּתַב עַל-אֶפְרַיִם וּמְנַשֶּׁה, לָבוֹא לְבֵית-יְהוָה, בִּירוּשָׁלִָם--לַעֲשׂוֹת פֶּסַח, לַיהוָה אֱלֹהֵי יִשְׂרָאֵל.||1 And Hezekiah sent to all Israel and Judah, and wrote letters also to Ephraim and Manasseh, that they should come to the house of the LORD at Jerusalem, to keep the passover unto the LORD, the God of Israel.|
Also, later in Chronicles 2 we see that King Josiah (Yoshiayahu) inherited the kingdom from the wicked king Menashe. Menashe had completely devastated the religious practices of the Jewish country, but when Josiah came to power he went on a rampage destroying all the idols that his father had erected or allowed to be erected. Once he was finished cleansing the land we are told that he then (Chronicles 2 35:1):
|א וַיַּעַשׂ יֹאשִׁיָּהוּ בִירוּשָׁלִַם פֶּסַח, לַיהוָה; וַיִּשְׁחֲטוּ הַפֶּסַח, בְּאַרְבָּעָה עָשָׂר לַחֹדֶשׁ הָרִאשׁוֹן.||1 And Josiah kept a passover unto the LORD in Jerusalem; and they killed the passover lamb on the fourteenth day of the first month.|
I think the answer can be found in the establishment of the holiday. Passover is all about us becoming the Jewish people solely because we follow G-D's commandments. This is seen by the original Korban Pesach. The Jews were differentiated from their Egyptian neighbors solely because they showed the sign, blood on the door post, that meant they followed G-D's command. There were no other significant factors that separated the Jewish household from the Egyptians household. Even if you were a Jew, if you did not have the sign on the door post, you were treated as a regular Egyptian.
This is why by Joshua, Hezekiah, and Josiah the Jewish people decided to celebrate Passover once they had returned to the service of G-D, because they understood the meaning of Passover.What is the point of the Tanach telling us that, specifically, at these times did the Jewish people keep Passover? There must have been many Passovers that the Jewish people kept that the Tanach does not mention. The point of the Tanach telling us that at this specific time, once the Jews had returned to the service of G-D, the Jews kept Passover is because of what Passover signifies. It is only when we are acting as the people of G-D that we are truly able to understand the meaning of Passover. Passover is all about realizing that you follow G-D because He is G-D. Did the idea that the blood on the door post would separate a Jew from an Egyptian make any reasonable sense? No, it was simply used as a divider of those who listen to G-D versus those who do not.
There might very well be reasons for the Mitzvos, they might all be logically explainable. This idea is a debate among many. (Rambam, Ramban and Maharal being a few) However, the most compelling reason to keep the Mitzvos is because G-D told us to.
This is the essence of Pesach. Pesach is a recognition that G-D is the one who freed us from Egypt. We celebrate the holiday because we recognize that G-D is our leader. Therefore, the Tanach emphasizes the celebration of Pesach only when the Jewish people recognize the reason and significance of this holiday. The Tanach is, in essence, telling us that this is how one should celebrate the holiday, because the commitment and zeal that these people are showing is the essence of the holiday.