Steve Jobs was Apple's Bill Gates. Tim Cook is Apple's Steve Ballmer - great businessman, but very little charisma or vision. It's remarkable how reliably these patterns repeat. Sundar Pichai is Google's Steve Ballmer as well.
I think Pichai is Google's Ballmer, but I don't think that applies to Apple at all. The better comparison for Cook is Bob Iger.
I think you're vastly underestimating the business acumen of Ballmer. His personal antics and lack of filter notwithstanding, he (and not Satya) is the only reason why Microsoft is a $1T+ company today: he was the one who started Azure and SaaS/subscriptions at Microsoft.