Well, one massive reason is in 1 Corinthians 2:12:
But we have not received the spirit which is of the world but the Spirit which is from God, in order that we might know the things that have been freely given to us by God.
I am a charismatic wannabe - I pray regularly for tongues, e.g. (and have not yet received it!). I have no doubt that God heals miraculously today; every day, I suspect. And so on. But what those of us who love the supernatural working of the Spirit in his more visibly startling manifestations must remember is that the NT paints a portrait in which these things are secondary: not irrelevant, not to be ignored, but secondary (note 1 Cor 13). The gifts of the Spirit must never eclipse the fruit of the Spirit (Gal 5). Better to be a loving cessationist than a proud charismatic. (But of course, best of all to be a loving charismatic!)
And I love how Paul puts it here in 1 Cor 2. The reason we have received the Spirit, he says, is in order that we might understand grace. The Spirit illumines the gospel. Pneumatology is for theologically-informed doxology.
Is it not possible for us to be truly born again Christians, experiencing the full manifestations of supernatural gifts in our lives, but be living largely moralistically, not living in wonder at the gospel? That was probably a problem in Corinth (1 Cor 12-14!). That is definitely a problem today.
God grant us a fresh outpouring of the Spirit, in both fruit and gifts--in that order.