I wonder if there's also an element of "easy street" about it - Klopp works our players hard, the style of our game is very intensive, as is the league. He might just be thinking that he could prolong his career at Bayern (and if a 33 year-old Lewandowski can top score there, then there's probably something in that). Bayern dropped 20 points in a 34 game season and won the league by 8 points. We dropped 22 in a 38-game season and lost the league by a point. There's more margin for error there, they don't have to be on it every game. There's also probably a sense that having worked for Klopp for so long that he's put his body through a lot of mileage in the last few years.
Same with Benzema in Spain. Madrid dropped 20 points and still won the league by 13 points. With Farcelona being in such a mess there's virtually no pressure there, and Ancelotti is happy to play Houllier-style football in the big games as we know to our cost.
Champions League aside, those guys don't play many tough games in a season and they can save their best for when it really counts (whereas last year our lads were running on fumes from mid-April onwards).
More money, less pressure, possibility of adding a year or two to your playing career. Guaranteed domestic trophies and a fair tilt at the CL. Sounds good to me.