Okay intercession falls under petition, as does penitence. And wordless adoration is, or at least implies, thanksgiving.
Some of us Catholics pray almost the entire Psalter every 4 weeks. My experience, having done this for decades, is that a psalm or a chunk of a Psalm will come unbidden but aptly to my alleged mind.
So, yeah, one can and many do pray rote prayers unconsciously. “We do not know how to pray as we ought.” But I don’t think they’re worthless. I may pray distractedly today what comes to my lips with power and urgency tomorrow. (Also, passages from scripture used as hymns or prayers are part of our daily practice.)
Jesus taught us how to pray