In the tract “Public Prayer” by John Newton, he admonishes us not to be irreverent in the manner with which we pray:

Contrary to this, and still more offensive, is a custom that some have of talking to the Lord in prayer. It is their natural voice indeed, but it is that expression of it which they use upon the most familiar and trivial occasions. The human voice is capable of so many inflections and variations, that it can adapt itself to the different sensations of the mind, as joy, sorrow, fear, desire, etc. If a man was pleading for his life, or expressing his thanks to the king for a pardon, common sense and decency would teach him a suitableness of manner; and anyone who could not understand his language might know by the sound of his words that he was not making a bargain or telling a story. How much more, when we speak to the King of kings, should the consideration of his glory and our own vileness, and of the important concerns we are engaged in before him, impress us with an air of seriousness and reverence, and prevent us from speaking to him as if he was altogether such an one as ourselves! The liberty to which we are called by the gospel does not at all encourage such a pertness and familiarity as would be unbecoming to use towards a fellow-worm, who was a little advanced above us in worldly dignity.

This reminds me of something I was recently reading by William Spohn summarizing Jonathan Edwards’ aesthetic:

The appreciation of God’s beauty has this ecstatic dimension; the person is absorbed in the “loveliness of divine things, as they are in themselves; and not [in] any conceived relation they bear to self, or self-interest.” In face of the mystery of God, the awe and respect of the tremendum balances the enjoyment of the fascinans. Edwards’ devotion was permeated with an undertone of deep reverence for the divine sovereignty; it never slipped into the chummy familiarity of pietism.

The fact that we address God the Father with an “Abba” is not supposed to tell us that we treat him like we would an old college chum, mere acquaintance, or even our own earthly fathers. It is meant to emphasize an expression of love and status as our sons, something, to be sure, which we should never take for granted with cheap expressions of flippancy, but with shock and holy amazement that we have been given such access–adoption as sons!–to the God of the universe, the God of Abraham, Isaac, and Jacob.