The Clays almost certainly thought that Klaus was actually The Other, not Lucrezia (And they told Beetle that). They might have gotten the info from Lucrezia herself. Setting up Klaus as the Other was a perfect bit of misdirection on her part. Klaus was off in Skiflander and she didn't think he could come back. A perfect patsy.
As for Klaus being a "Benelolent Tryant", he is. And he HATES the job. The reason he grasps so much to power is he doesn't trust anyone else with it, not because he likes it. Many sparks are meglomaniacs who go and start wars, turn superweapons on armies or create monsters (even by accident). They are people NOT to be trusted to hold a seat on an empty bus, much less with any real power.