Why did he leave Basle?
Similar to the situation here, although much less acrimonious.
Unlike certain other managers, he finished his contract. And unlike certain other managers he accomplished everything he set out to do, having won the League and doing extremely well in Europe. Also unlike certain other managers he was pretty adamant while there that he was happy and not leaving until his contract was up.
But he and several of his players had become high profile enough that they could move on to bigger things. I don't think Basel could have paid them enough, and they still have enough to win their league. I think it was just sort of in everyone's best interests to part ways.