When I became a Christian (1979) I attended an Assembly of God church in Harrison, NJ. A "prophetess" came to speak and baptize people in the Holy Spirit (the second blessing), accompanied by receiving the "gift of tongues". Forget for a moment that Eph. 1:3 tells us that we have every spiritual blessing in the heavenly places, in Christ, ergo we lack nothing for the practice of our Christian faith. Intuitively I knew that there was something wrong praying in an unintelligible language that my mind did not understand. Even though I was a new Christian, I understood plainly from the Bible that tongues was speaking a known language you did not previously know. As I matured as a believer I was taught hermeneutical principles by a godly pastor. He taught me that when there is one plain, normative passage on a matter, and one vague passage on the same matter, interpret that vague passage through the plain, normative passage. Acts 2 is the plain, normative passage on tongues. The tongues spoken on the day of Pentecost were known languages. The tongues spoken in 1 Corinthians 14 are vague. Is it an ecstatic language? Is it a known language? Christians on both sides argue. The plain, normative text in Acts 2 adds clarity.
Another a problem with a private prayer language is that a) there is no interpreter b) there is no warrant in scripture to pray in such a manner c) Rom. 8:26 is grossly ripped out of context by Continualists d) there is no benefit to praying in a private prayer language that your own native tongue cannot provide. When Paul wrote " In the same way the Spirit also helps our weakness; for we do not know how to pray as we should, but the Spirit Himself intercedes for us with groanings too deep for words;" (Rom. 8:26), he was simply saying that because of our sin and human frailty, we sometimes do not even know what to pray. I have been like this when broken by my sin and have experienced something profoundly emotional. God knows our heart even when we do not know what to say.
Back to that "prophetess". I was told that Christians who receive the second blessing and speak in tongues are closer to God. They have something that other Christians do not. I understood that this created a caste system within the church. Verbalized or not, there was this reality that "I have something you do not." When I came to that realization I left charismania.