Grace & Peace!
I would say that the power in these traditional prayers is twofold:
1–Lex Orandi Lex Credendi: the Law of Praying is the Law of Believing. That is, what we pray and how we pray it informs our faith. Our faith is a reflection of our prayer–moreover, our prayer gives us the faith by grace which we in our sinfulness may lack. If our prayer is a reflection of our faith, then we have closed the loop of grace and our belief merely self-reflexive. This isn’t an argument against “freeform” prayer. But an argument for freeform prayer informed by tradition. We learn to pray and to believe by praying the prayers of the church, the greatest of which is the Eucharist.
2–In praying these traditional prayers, one unites oneself with the Communion of Saints–we pray with the church, we make the church’s mind our mind. One does not merely follow tradition, but lives the tradition by praying the prayers which reflect the mind of the church at prayer. One truly engages with the reality of the 8th day of creation, the renewal of which the Church is the living symbol and reality.
The power of the traditional prayers is not magical in the sense in which the word magical is commonly understood–they are not magic words which must be perfectly recited in the original Latin in order to have the proper effect–prayer is not an act of works righteousness which is done apart from grace. But it is possible to see these prayers as sacred formulae, tried and true, for accessing the sacred, doorways to the sacred realities of grace which by grace have a real effect on the disposition of the soul to grace. So why not endeavor to use these doors to the palaces of holiness which have been given to us through the Church by the Spirit of Holiness himself?
Under the Mercy,
Mark
Deo Gratias!