This guys got both star power and conservative bonafides. Can you imagine a debate between him and the Hildebeast? He would publicly eviscerate her and still come out looking like the good guy.
He's an ACTOR. Now, that may be obvious, but his skills, as you mention would be priceless.
Hillary stumbles, pauses, forgets what to say, backtracks and screeches.
Thompson can MEMORIZE what needs to be said and deliver it thoughtfully with conviction and passion that can stir the listening audience.