Well, what it has brought to mind for me is the command to "pray without ceasing". I have actually tried to cultivate that, or at least a constant attitude of prayer, for ten or twelve years without really all that much success. As long as I keep my attention focused, I can, but I can't go about my day like that.
Much of the Divine Liturgy IS prayer. And the simpler ones especially can play like background music in my mind all the time now. It serves as a strong reminder - a very strong reminder - that we depend on God for all things, and always appeal to His mercy.
So yes, I think constant prayer has it's benefit.
I'm not arguing against repeating God's promises, His acts and attributes, or praise to Him. That's part of the prayer too, especially His acts, attributes, and praises to Him. It's all intertwined, and all beneficial to me.
It's hard to explain ... but just imagine if your spirit can pray/repeat those kinds of things continually to your consciousness much of the day. It's ... just very beneficial. I'm not sure if that is the what the chant is designed to do, but it wouldn't surprise me. The hesychastic tradition seems to understand quite a bit about this kind of thing, and the Church does just about everything for a reason.
(Don't get me wrong, I am a big fan of good worship music as well, and it has done much to lift my spirit to God, but this is just different.)