Companies take on the behavior of the personalities of the people at the top. Nadella, like Gates and Ballmer before him, was selected based on shrewdness, and everything flows from there. It's simple. The company will continue to bear the culture born of Gates because of their board (at the top), and their HR department (everywhere else).
However, shrewdness is just one trait, and I think it's disingenuous to insist that we can reasonably ignore all other consequences of having a different human being running the company because their shrewdness makes them as interchangeable as planks on a wooden boat.
Personalities and management philosophies can't be reduced into some simple measure on a shrewdness scale, and the other differences between these real human beings that you don't seem to be taking into account can and do bring real change in how the company behaves and operates. Maybe not a lot of the change is concentrated on the axis that you've cherry-picked, but that doesn't mean we can dismiss all the other change that may have resulted from this change in management as "next to nothing".
They in fact back fill the role with someone they think should be in charge of the future of the position (which is very often in a radically different direction), or more often than not eliminate the role altogether.
By your estimation, when Steve Balmer retired, the board would have hired another Steve. No, that's not the case. They hired Nadella who is different.
Microsoft still sells (almost) no hardware, PC sales are dropping like a stone, corporate sales are lagging (my Fortune 150 switched to Windows 8 a YEAR after 10 was released), and Microsoft has to monetize seats of Windows somehow. What's left? Collecting and selling user data and advertising. This sort of thing has to have been approved by Nadella. Is this the move of a "kinder, gentler" CEO who just loves open source and freedom? No, it's a move by a shrewd person who is desperately trying to keep his company relevant in the face of phones, tablets, clouds, and social media.