Context is needed for proper understanding
We need to look at what Paul had in mind in the 3 passages you mentioned, and ask this question: "What exact pairs were Paul contrasting, and what was the reason?" We will find that it's not Biblical exegesis / theological training per se, but whether those training will prevent us from coming to faith in Christ as our Lord and Savior:
- In Phil 3:1-11 the contrast is between Judaizers who required circumcision (v. 2, which is a work we do) and true faith which requires God's grace (v. 1, which is what Christ did, v. 7). Verse 8 you mentioned is comparing Paul's meticulous obedience to the law (v. 7), which he claimed was superior to a typical untrained Jew, which then became a source of pride to some Pharisees like him. But here, Paul was not faulting his training, but faulting his pride and reliance on observing the law which made him blinded of the necessity of God's free gift in Jesus.
- In Acts 22:1-23, Paul again was contrasting his zealous observance of Jewish laws and custom (v. 3) as well as his commendation from the highest authorities (v. 5) with the power of baptism of Jesus and the power of faith which washes sins away (v. 16). Paul was also contrasting his old mission to persecute Christians (v. 4) with his new mission to spread Christianity to the Gentiles (v. 21), commissioned directly by Jesus himself, which made him persecuted and imprisoned at least 3 times. The reason for the contrast, again, is the same as in Phil 3:1-11.
- In 1 Cor 2:1-16, the contrast is between "lofty words and impressive wisdom" which Paul deliberately did not use (although he could have done so, such as in writing Romans) and the "plain message and preaching" (v. 4) of the gospel. Paul did this to let the Holy Spirit receives the glory when his audience converted (v. 4b-5). The second contrast is when Paul was discipling mature believers (v. 6): between the "wisdom that belongs to this world" (v. 6b) and "wisdom of the mystery of God" (v. 7) given to the apostles (v. 13). Again, Paul here is not faulting his training, but condemning those who, despite hearing the wisdom coming from God, refused the Holy Spirit who could have explained that mystery to them so they became Christians (v. 11-12, 14-16).
Proper modern day use of scholarship and modern religious degrees
From these 3 passages it is clear that Paul was condemning the learned teachers of religious laws, the scribes, the rabbis (Pharisees) and the rulers (Sadducees) who (because of their training and their hardness of heart) rejected the gospel, crucified Jesus, and persecuted Christians afterwards, including Paul himself (prior to his conversion)! Remember that not all learned scholars in Jesus's day rejected Him; Nicodemus being a prime example (since he wouldn't be eligible to be member of the Sanhedrin if not for his training in Jewish law). The modern counterpart of the ones condemned by Paul include non-Christian New Testament scholars such as ex-Episcopal Bart Ehrman, liberal Episcopal Bishop John Shelby Spong, John Dominic Crossan, Orthodox Jew Amy-Jill Levine, former Catholic nun Karen Armstrong, etc.
But after conversion, Paul used his theological and exegetical training to defend orthodox (i.e. apostolic) Christianity which he contrasted with the false teaching of the Judaizer, mischaracterizing freedom under God's grace by continual sinning, overly charismatic believers who did not love, proto-gnostic beliefs, over-realized eschatology, etc. Many scholars consider the book of Romans to be the first systematic theology; a book that could only be written by someone with Paul's training in the Hebrew Bible, someone who could link proper OT interpretation with Jesus's teaching. Thus Paul's interpretation of the OT and the gospels has for almost 2,000 years become the benchmark, along with interpretations by key church fathers such as Irenaeus, Origen, Athanasius, and Augustine.
Exegetical and theological training (via modern day religious degrees such as Master of Divinity) is critical to prevent the faithful from inadvertently being led astray by bad doctrines (such as prosperity gospel, syncretism, modern day Gnosticism, non-Trinitarian Christianities, etc.). One common way today is to require pastors to graduate from accredited seminaries so:
- their sermons are more grounded in proper exegesis
- by surveying various theologies they know where their church stands in contrast with other denominations and understand the relative importance of doctrines (Trinity being the highest)
- they can shepherd their members against subtly wrong theology or wrong application of theology to life
- they learn pastoral theology that help them develop discipleship programs
- they learn administrative and organization skills in shepherding a local church
Please note that evangelism and acceptance of the gospel does NOT require scholarship (cf 1 Cor 2:4) but simply require intelligent reading of the Bible with an open heart and with the aid of the Holy Spirit. Devotional reading to cultivate one's relationship with God also doesn't require scholarship.
But when Christians become divided over different interpretations concerning live issues that affect their spiritual lives such as the need for praying in tongue, credo vs. pedobaptism, abuse of tithing, claims of prophecies, etc. scholarship can be a good resource for civil discussion in Christ to promote common understanding while being honest about remaining differences. One recent result was a 2019 book by Brett Salkeld Transubstantiation: Theology, History, and Christian Unity which shows that Aquinas, Luther, and Calvin were not that much different in their understanding of the real presence in the Lord's supper, which effectively bring Catholics and Reformed Protestants closer together.