A whole lotta ink (both digital and actual) has been spilled over the issue of Paul’s use of αββα. While I am not going to rehearse here why “αββα” isn’t “daddy”, I will make one comment that I have not heard scholars make about Paul’s use of “αββα” in Romans 8:15.
A plethora of scholars hold that the letter of Romans was written to a mixed congregation of Jewish and Gentile Christians (although the latter made up the majority). Paul’s purpose in writing the letter is not only to promote solidarity with the Roman church and raise funds for his trip to Spain, but also to build church unity. Paul’s exhortation to the stronger to give up their rights on behalf of the weaker lends credence to the idea that in-house debates between Gentiles and Jews over food laws were promoting disunity rather then love.
For this reason, when Paul comes to chapter 8, before his middle section concerning the place of Israel in the purposes of God, Paul describes our status as sons and daughters because of the Spirit of God (and not because of our ethnic status). Paul uses the common Christian name for God in the two languages used in the church (Aramaic and Greek) to unify them around their common God. Although Christians may use the term today, there is nothing magical about the term. You may as well say πατηρ!