Just read this chapter and found anew in verse 28, that uninterpreted tongue-speaking ought not be in public worship, but for times of private devotion with God. Interpreted tongue-speaking ought to be allowed, though (vs 39). I can't say I've seen this done in a worship service. Charismatics seem specifically to need to hear this one chapter of the Bible that speaks most of the gift by which they distinguish themselves.
The broader issue for charismatics is that they associate the Spirit with sensational and super-natural happenings. This is a false/partial association. The Spirit produces "everyday" virtues and spotlights Jesus, not Himself. He typically brings about signs and wonders and super-natural events when He points to new revelation from God, as given at the Exodus, with prophets, Jesus, and the early church, to assure believers of this new revelation and to edify the body.
This is not to limit God's supernatural activity today. I believe he does heal by supernatural means. But has he given the spiritual gift of healing to Benny Hinn, or any other specific person today? I don't think so. But he gives healing and "mystic, sweet communion" with Him as He will, even now. And to go one step further, never having been on the mission field, He may give such supernatural signs through missionaries to a society in the grip of demons, to release those demons' hold on a people and let them see a stronger spiritual power than the spirits or the medicine men. The missionaries I've talked to say it's an act of faith for animist natives to take western medicine for illness. It is renouncing their belief in the local gods or medicine man. So conversion to God in such settings can also happen without "supernatural" signs and wonders, if the Spirit changes hearts within.
(11 references to the Old Testament in 1 Cor 14)