Visual thinking, a more closely related subset of diagrammatic reasoning (which need not be visual, incidentally), is in no shape or form "privileged". Visual thought is in fact closer to the general form of thinking that might be found in other sentient creatures who are not "privileged" with human language. Stated another way, diagrammatic thought is closer in shape and form to domain general pattern recognition. Reasoning, or "illation", is of a peculiarly non-linguistic nature, such that you'd be hard pressed to point out, like Achilles, to the Tortoise, just what it is that makes a conclusion of reasoning one that necessarily follows from some set of premises, unless you made use of some diagrammatic method.

Not sure why you're arguing a priori that all thought must be "vernacular" - code for "linguistic", I'd assume. But thought is not merely verbalizing or grammatizing everything.