There is a legit requirement for us to be able to audit, but placing the other conditions on it makes it, at the very least, unreasonable but the "without notice" bit means that if they agree to it we have can disrupt their business at our leisure (since an audit requires their resources to conduct too).

another example is requesting infeasible levels of application logging, insane retention periods, and onerous evidence that they're acting on that information.

Sometimes these riders serve a purpose (Van Halen's case), sometimes they are indeed a caprice, or a joke. If I recall correctly it was Pearl Jam, who once demanded their M&M's to be segregated into jars, and each jar could only contain one color of a candy. There were photos floating around the net with the band members laughing and posing with that jars and the guy who felt into the trap. Oh, life of a rock star ;)