If repeating words of prayer is babbling because the mind ‘disengages’, where do worship songs fit in?
Regarding worship, we must be careful to distinguish repetition from mindless chanting. Repetition in Scripture is a heathy and normal way to reinforce a truth. Remember, the worship that takes place around the throne is repetitive to a degree:
Rev. 4:8 And the four living creatures, each one of them having six wings, are full of eyes around and within; and day and night they do not cease to say,
“HOLY, HOLY, HOLY is THE LORD GOD, THE ALMIGHTY, WHO WAS AND WHO IS AND WHO IS TO COME.”
So repetition in worship of proper doctrine or other truths is appropriate and shouldn't be rejected simply because it doesn't appeal to us. Repetition of mindless phrases that are not especially edifying may not be as helpful. Each worshipper should decide for himself or herself in this matter.