Agreed.
And all competent Cognitive Therapy and CBT practitioners are supposed to collaborate with the client to develop an individualized cognitive-behavioral case formulation with varying levels of generality of 'problematic patterns of thinking' including the automatic thought (surface, event-specific) level, the intermediate belief (rules/attitudes/assumptoms) level and the core belief or schema level.
It doesn't really get much 'deeper' than a schema (core belief) of 'I'm unlovable' or 'I'm incompetent.'
Of course, a comprehensive biopsychosocial case formulation takes in a lot of types of data for consideration including biological variables, developmental variables, hell, even an existential perspective/ variables at times.
But calling CBT, on its face, 'not 'deep' enough' as an approach is really betraying one's ignorance about the approach to begin with. And the older books/ articles on cognitive therapy and CBT were a helluva lot more 'theory rich' than most recent approaches and the field has come to over-represent manualized approaches to courses of therapy and worksheets and under-emphasize flexibility, individualized case formulation, the primacy of the working relationship, collaboration, etc. to the detriment of the entire field. There is some recent push-back against the 'protocol-for-syndrome' approach, but I don't see it being appreciated by most practitioners, currently.