Rabbis and sages ask "Why is the Succot Holiday celebrated a couple of days after the Rosh Hashannah-Yom Kippur block of Holidays?"
My answer has a linguistic base. Many of the prayers during Rosh Hashannah and Yom Kippur mention G-d as מלך "Melech," King. The word סוכה "succah" has the same root as נסיך "naseech," prince, or anointed one. G-d, the King, has a מלכות "Malchut," Kingdom, while David, being a person, a descendant of the most "human" of the tribes, Yehuda, who has the power, the ability, not only to sin, but to apologize to both Man and G-d, to admit mistakes, to do תשובה "tshuva," to return to G-d in repentance, has a hut with a green roof, a succah, not a permanent palace.
I live in Shiloh, where the Mishkan, the portable Tabernacle stood for 369 years, while we waited for a leader, for a king who had the vision to lead us to Jerusalem where the Beit HaMikdash, the Holy Temple would be built.
When David finally ruled, he went to Jerusalem, but G-d wouldn't let him build the Temple. His son, Solomon, Shlomo HaMelech did. But Shlomo, with all of his gifts and talents couldn't sustain the spiritual level needed, and he sinned, as he relates in Kohelet, Ecclesiastes.
The first Temple and then the second were destroyed.
G-d willing we will reach the required level to build the Third "speedily in our days."