Customer-centricity is an organizational point of view, not a customer point of view. It’s actually the organization-centric-view-of-the-customer.
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Don’t you want CRM to help you and the customer mutually, allowing you both to manage the relationship? Surely the value of your understanding how influence goes around comes around is enhanced when those you interact with have similar understanding. Or would you rather propagate the status quo – CRM as a construct to manage the customer?