We have a manager who very much sees the human aspects of a footballers life as well and if Clyne expressed a desire to play regular football then Jürgen likely wanted what was best for the player and thought the impact on the squad can be coped with.
He treats players like human beings and we only see it from a fans viewpoint while those within the club have to look at the bigger picture.
I hope you are wrong that that's how Jürgen operates. His overriding priority must be the team and its overall strength, f**k some fringe player who wants to leave a few months before his contract expires, just tell him to shut up and do what he's paid to do, be ready to step in when needed and in the meantime work hard in training and try to win his place back.
I suspect Klopp's weakness is that he is a bit to much Mr Nice, but in football you need to be tough, the very best managers always are, Shanks, Paisley, Fagan, Ferguson, Maureen etc etc. None of them would have accepted weakening a squad's strength just so that a squad player can get some more game time.
The very best managers are excellent man managers, but that doesn't mean being soft and giving in to all their requests, it means being tough but fair, like a parent and always thinking of the team first, then the player.