I have never seen Ann Coulter win any debate because exactly of what you described, total immaturity in her debating style, smirks and snide looks, sarcasm in every word, silly and stupid jokes, and she thinks this is the way you win a debate with a liberal. But of course according to her adoring fan on FR she rivals Cicero with her debating skills.
Ann Coulter has come up with a successful marketing strategy and it works every dang time. The MSM gives her all kinds of free press after she says something outrageous. And the people who don’t have the depth God gave a blade of grass snap up her schtick and her books like candy because of who she angers. Every time — outrageous comment, spinal cord howling and free press, spinal cord reaction to buy her cartoonish books.
The only difference between her and the “artists” who dunk religious artifacts in dung and urine is that she is far more effective at making money out of being a complete tool.