I believe if we put Trinity out of it, then the 'son' analogy sounds valid and actually meaningful, and this is even consistent with the teachings of Islam.
From examining the critical verses of the Quran in relation to the Christian view of Jesus, it appears that the reason Allah rejects the Christian idea of "Jesus being son of God" is because divinity is a presumed part of the concept according to the Christian view and Quran clearly rejects the belief in Trinity and divinity of Jesus in 4:171 and 5:72.
Despite that, as you mentioned, Quran does recognize the miraculous birth of Jesus and that he was "a word of Allah" (examples: 3:45, 2:171).
Therefore, if we purge the filial analogy of the concept of the Jesus Divinity, the Trinity and also of its literal connotations, then there would remain nothing fundamentally wrong with using the metaphor. In fact it can be used meaningfully as a metaphor for the relationship of human beings to the creator.
It is important to notice that even in Islam our relationship with Allah is also described with metaphors/analogies. According to the Quran, we are 'servants' or 'slaves' of Allah whereas in Christianity we are 'children' of God. And in both religions the messenger is considered to be the best example of that relationship.
Therefore, it seems that the whole concept of son-father in Christianity -- whether applied to Jesus or Christians -- was originally meant to have a similar function as does the Islamic metaphor of master-slave, but has been twisted as in the Nicene Christology beyond its intended meaning, despite the fact the Homoousian interpretation of the son-father relationship is nowhere explicit and elaborate in the Bible. This critical view of mainstream Christology has inspired the modern Unitarian movement.
A different variation of son-father metaphor has also been common among Christians and Jews alike, denoting their special relationship with God as His 'sons' or 'children'. This notion is mentioned in Quran 5:18 which reads:
The Jews and the Christians say, “We are the children of God, and His
beloved.” Say, “Why then does He punish you for your sins?” In fact,
you are humans from among those He created. He forgives whom He wills,
and He punishes whom He wills. To God belongs the dominion of the
heavens and the earth and what lies between them, and to Him is the
This notion of son-father relationship must not be confused with the literal notion as in the concept of God the Son in the Trinity. Also this verse doesn't imply a denunciation of the doctrine of sonship itself but its wrong or misapplied connotations. These are the points that Allahme Tabata'ei stresses in relation to this verse in his authoritative al-Mizan Exegesis on Quran:
Certainly, they did not claim real sonship as the Christians claim for
the Messiah (a.s.). Neither the Jews nor the Christian put forward
this claim in the literal sense. They called themselves sons of God
metaphorically, as a mark of distinction. In their scriptures, a lot
of people have been called sons of God, for example, Adam, Jacob,
David, Ephraim, Jesus, and good-doing believers.
What they meant with this claim was that their relationship with
Allah was like that of sons with their father. They thought
the sons of a King who had special status in comparison to the
subjects. ... This claim of special relation and belovedness was meant
to establish its inseparable attribute, that is, they can never be
chastised and punished. They are assured of Divine favor and honor
because if Allah were to punish them, it will go against the
distinction and honor that He has reserved for them. The proof of the
above interpretation is seen in the rebuttal of their claim where
Allah says: He forgives whom He pleases and chastises whom He pleases.
There was no reason to give this reply if they had not meant by their
claim: "We are the sons of Allah and His beloved ones", that they
cannot be punished at all even if they did not accept the call of
truth. Also, there would be no meaning to the statement: Nay you are
men from among those whom He has created. In short, when they said:
'"We are the sons of Allah and His beloved ones'", they wanted to say
that they were the chosen people of God and His beloved ones and Allah
was not going to give them punishment even if they did what they did
or left what they left, because full security against every unpleasant
result or situation was a concomitant of special relationship and
love. al-Mizan Online
The "Father-Son(s)" Spiritual Kinship vs "Master-Slaves"
[An Off-Shoot Discussion]
Now considering the existence of valid notions of metaphorical descriptions of God-human relationships in both Christianity and Islam, another relevant question may follow: which analogy/metaphor better describes our relationship with Allah/God?
In Christianity, Jesus birth by the Holy Spirit into Virgin Mary provides a very valid basis for using the 'son' analogy for him. Also considering that even in Islam, according to Allah's Names and Attributes, Allah is considered to be our benevolent provider and take-carer (as in rahman, razzaq and rab) and also guardian and protector (hafiz)—attributes that characterize fatherhood, there seems to be a valid basis for the father-son analogy.
However, a discerning analysis reveals that the 'slave' metaphor denotes additional meanings in regards with the nature of our relationship with Allah, as Allah is also considered to be our 'owner' (malik) and 'patron' (wali), 'subduer' (qahhar) and 'humiliator' (khafis) that characterize a master-slave relationship.
This observation explains why even the valid notions of the filial metaphor has been abandoned by Islam in favor of a master-slave metaphor which encompasses the filial characteristic and therefore excels in denotative richness.
To further the implications of this discussion, the concluding observation can be regarded as a supporting argument for Islam's claim of superiority over other religions as being the most manifestly all-inclusive of God's names and attributes as denoted by His greatest name, Allah. Imam Ayatollah Khomeini a master of esoteric sciences and gnostic commentator ascribe the superior status of Quran as a Divine Revelation to being an emanation of God's Greatest Name:
the appearance of the Qur'an follows the “Collective Appearance”
[zuhūr-i jam'ī] of the Divinity and the Contraction [qabd] and
Expansion [bast] of “Mercifulness” [rahīmiyyat) and “Beneficence”
[rahmāniyyat]. Rather, the truth of the Qur'an represents the level of the
appearance of the Greatest Name of Allah through the appearance of
“Beneficence” and the “Mercifulness,” and is “inclusive of the
the general and the differentiated” [jāmi'-i jam'u tafsīl. (Disciplines of Prayer, italic words represent translation improvements and are mine).
While full comprehension of the passage demands a deep knowledge of the individual mystical concepts and related theories, the passage is basically pointing to the merit and superiority of Prophet Muhammad and His religion over other prophets and religions by introducing it as an inclusive manifestation of Allah's names.