the Bible was fine with what title of Allah being abrogated due to its association with shirk?

"Baal".
This title, although conveying a certain meaning (similar to "Lord" or "Owner" — one which always applies to Allah), became associated with shirk and the people of shirk. The currency of the word itself had been misapplied, with the worst of misapplication and counterfeiting.
So, to separate from that misapplication and those misapplying it, the use of the term "Baal" was abrogated for the believers (although the meaning still applied).

This makes a clear precedent for what would occur later with the Biblical traditions. The terms "Father" and "Sons/Children/Daughters of God" are alleged a certain currency, not a "literal fathership" or "literal offspring", nor how it is taken by Christians today. See attached for the Jewish understanding of the latter term.
These understandings convey a certain meaning — regarding God as the Protector, Provider, Author and Source of Life: and regarding His Servants as those who have received life and provision and protection from Him.

Like "Baal", the currency of these words — "Father", "Sons/Children/Daughters of God" — had been misapplied, with the worst of misapplication and counterfeiting. Although they would have been (originally) understandable with the same meaning that Muslims hold of Allah today, the case for separating from their misapplication (by abrogating them) has a clear Biblical basis.

Any Christian criticism attempting to highlight the absence of these terms is really highlighting the consistency of our position with the core (monotheistic) Prophetic traditions.