A better King position in Endgame was decisive

The king position in an endgame can become the decisive factor. It  can make the difference. Please look at the following position. It is a postmortem analysis of one of my own games:

The better position of the white king is eye-catching! Also obvious is the "bad" combination of the dark-coured pawn chain a7-c5 and the Bc7. I decided here to offer the exchange of the bishops cause of his better king position

And here one that is very similar. No one less than former worldchampion Kasparov played with the  the black pieces and used the better position of his king for an exchange of the bishops and a win