His disdainful view of the value of rhetoric and vicious hostility to the achievements of high culture, or the use of language in artistic ways to express in more aesthetically appealing ways thoughts that can be expressed more "simply" toward largely semantically equivalent ends (from an empirical perspective, anyway) also rubs me the wrong way.
I mean, sure, saying something as tersely as possible is often valuable and a good lesson to teach. It is also often the wrong thing to do or, more likely than being flat-out wrong it simply has costs as well as benefits. What precisely those are depends on what you're trying to achieve with your writing.
Should one take Dr. Covington's suggestions when writing a novel, an interesting anecdote, or a persuasive expository essay, even if one is otherwise partial to the goals of clarity in the thinking and writing that goes into it? Do most writers we consider interesting, compelling, thought-provoking, intriguing, entertaining, etc. follow his stylistic suggestions? Would their writing conserve those essential qualities if they did?
In short, while his objectives may be good lessons for people that write in unclear, logically incoherent or circumlocutory ways, he seems to tend toward very extreme reductions. It is a necessary part of intellectual development to learn to grapple with the complexity that inheres in many facets of existence, and that includes gestalt complexity that cannot be reduced to very simple atoms as, for example, in the ontology Functional Programming preaches. The world is not a giant software construction.