2 problems with this.
First I’m not sure 2 qualifies as multiple leagues but certainly the CL stage I’d say your essential criteria would have ruled out Klopp himself.
Second Klopp has worked hard to create something here. There is a good solid base like what Shanks left Bob or more recent Rijkaard left Pep at Barca. What we’re looking for is evolution not revolution. Build on what had been put in place and progress it to the next level. The kind of managers you are talking about have their strict blueprints for how the club would have to change to fit what they would want. Different playing styles, tactical set ups, dressing room culture. Could you imagine someone like Mourinho coming here? It’s nightmare fuel. It’d be chaos. A younger, up and coming manager willing to learn and adapt into the structure (and there’s already some similarities between his set up at Rangers and Klopps at Dortmund actually). If they have the right ability? Surely the manager equivalent of if they’re good enough they’re old enough?