Daniel 4 is about God's Kingdom and right to rule over mankind which means sovereignty and Nebuchadnezzer confessed to this simple fact after the end of seven years of abasement. The dream has several features that prove that it has a far greater significance becaus ethat kingdom was yet to be a reality in men's affairs awaiting the arrival of Jesus Christ to be installed by God as Ruler of that Kingdom for this is proved by the prophecy in Daniel 4:17.,
Actually, all of the Aramaic apocalypse of Daniel concerns God's kingdom and the authority he gives to men to rule. That's the theme that runs through the Aramaic section as a whole (2:21, 37-38, 44, 3:28-29, 4:2-3, 22, 25, 30-32, 34-35, 37, 5:18-23, 6:26-27, 7:18, 26-27). The stories concerning Nebuchadnezzar and Belshazzar in ch. 4-5 illustrate the point made in Daniel 4:17 that "the Most High is sovereign over the kingdoms of men and gives them to anyone he wishes". Compare 2:21: "He sets up kings and deposes them". God gave Nebuchadnezzar all his power and success (2:37), but ch. 4 shows that he could just as easily take it away or give it back. The same theme is found in ch. 5, which reiterates the story in ch. 4 and relates how Belshazzar lost his kingdom because he did not acknowledge God. The apocalyptic material in ch. 2 and 7 (which are largely parallel surveys of history) is what "prophesies" that the fourth kingdom will be the last until God replaces all these kingdoms with his own rule. The stories about Nebuchadnezzar and Belshazzar reinforce the point that God delegates authority to whom he pleases (whether it is to Darius from Belshazzar in ch. 5 or to the saints of his people from the fourth kingdom in ch. 7), but they are not eschatological prophecies in themselves. Why does the Society extend Daniel's warning to Nebuchadnezzar to refer to distant future times (e.g. 1914), but not his warning to Belshazzar in the next chapter? Why does the former supposedly point to the "last days" but not the mene-mene-tekel-parsin warning? There is nothing in the text itself that points to anything beyond the application that the writer himself gives, i.e. to Nebuchadnezzar himself.
Your argument that the tree dream is nothing more than a chastisement of a king overlooks the blatant fact that the entire chapter is about the Kingdom of God and Sovereignty which Nebuchadnezzer confessed as to its reality so it is not surprising when you obscure this fact then you see nothing more than a simple story.
The story is not about a mere chastisement of a king. It is about how what happens to Nebuchadnezzar foreshadows what happens to Belshazzar in ch. 4 and what happens to the fourth kingdom in ch. 7. But recognizing this literary connection is altogether different from allegorizing the story to turn it into a chronological cipher of the "last days". The "Gentile Times" pesher pursued by the Society doesn't even make internal sense. Nebuchadnezzar is the Gentile king who brought the earthly representative of God's kingdom to an end, and yet it is the incapacitation of Nebuchadnezzar that is made to symbolize not the cessation of Gentile rule but Gentile hegemony over the earth, such that the return of this Gentile king to power is supposed to represent the end of the "times" of Gentile rule.
Further, in proof of the fact that iddanim means 'times' is supported by the footnote in the Hermeneia commentary on Daniel by John Collins which I have referred to in a previous posting on this subject.
Actually, Ginsburg (Studies in Daniel) noted that khronos "time" was used idiomatically in the sense of "year" in Greek (referring to counted periods of time used to compute dates) and suggests that 'iddan reflects Greek idiom (just as ch. 3 contains a few Greek loanwords into Aramaic). Then when Daniel was translated into Greek (the OG version), kairos was employed instead of khronos as the term equivalent to 'iddan.
In fact, Jesus as recorded at Luke 21;24 used kairos and not chronos as you falsely allege and by the use of this word and the context of Jerusalem which typified the Kinngdom of God- the theme of Daniel 4 certainly connects well exegetically with the seven 'times' of Daniel 4.
Luke 21:24 is allusive of Daniel but not the kairoi from ch. 4 but the kairoi mentioned in ch. 7 (specifically 7:25), the chapter that is actually depicting the establishment of God's rule on the earth. The use of the verb "trample" is especially linked linguistically to ch. 7. The 3 1/2 times of ch. 7 is midrashically interpreted in ch. 9 (from the Hebrew apocalypse of Daniel) as the final portion of 70 weeks of years, the half-week during which the Jerusalem sanctuary is desolated with war and abominations. The author of Luke has this whole period in view as the "times of the Gentiles", as it is precisely a period when Jerusalem would face "times of trouble" and desolation. The language in ch. 21 of Luke reflects both ch. 7 and ch. 9 of Daniel.