That's opposite my experience: I took an appointment a few weeks ago from my insurance agent (Texas) who wanted to review my existing insurance vs my needs. On the call I laid out that same logic -- I can afford repairs to my car out of pocket, so it doesn't make sense to insure it, so maybe I should drop it (just keep liability) -- and she agreed, and was happy to tell me the savings!

(I didn't go through with it on the call and maybe she would have put up resistance then, so who knows.)

Edit: From reading the source, it seems like the author didn't clarify that that was the logic he was using, or that he could afford the damage to his car out of pocket. Insurers are probably accustomed to people overextending themselves and skimping on insurance without being able to afford such things, which is risky and something agents have to head off early on.