That title is really the only eye-raising aspect of Leander Kahney’s latest book, which is a timely and much-needed look at the post-Jobs Apple.

And to be fair to Kahney, Cook has absolutely taken Apple to the next level despite his inability, thus far, to create another iPhone-level hit. Apple under Cook has emerged as one of the richest and best-run companies on earth, a customer-centric powerhouse that vexes critics as much as it delights fans. But Cook is correctly judged not just by his stewardship of the foundation laid by his predecessor, but also by the parts of Jobs’ empire that he’s dismantled. Today’s Apple is far more empathetic, charitable and, yes, open then before.

As a student of history, and of personal technology history specifically, I’ve long gravitated to industry books that focus on individual companies like Microsoft, Google, and Apple as well as platform wars such as Windows vs. Mac, Android vs. iPhone, and various video game console generations. Some are worth reading again and again, and some are fascinating simply because they provide a cohesive take on a certain era or event.

Tim Cook at the very least falls into the latter category—we’ll need to see whether it stands the test of time—by offering what I believe is the first in-depth look at Cook’s Apple. The timing is a bit tough, to be sure: Apple Watch and its health-monitoring prowess is just starting to gain steam, and Apple just this past month launched a sweeping set of services that will or will not make up for a slowing iPhone business.

No, Mr. Cook didn’t speak to the author, nor did most of Apple’s senior leadership, at least not on the record. But we still get a lot of good—and, I think, new—information about crucial events of the past decade thanks to good reporting and the anonymous Apple executives and employees who did speak with the author.

For example, there’s a great passage about Cook’s decision to deny the FBI access to an iPhone that was used by a domestic terrorist, with Kahney reporting on Cook’s disappointment that the case never went to trial: He really wanted to make a public stand on what he saw as a crucial moral point.

I was just as interested in the in-fighting and politicking that led to executive Scott Forstall’s ouster by Mr. Cook. Forstall, a Jobs favorite and a presumed future Apple CEO, presided over the back-to-back failures of Siri and Apple Maps and then refused Cook’s demand for a public apology. So he was fired, and Cook’s Apple went on to publicly apology for a number of issues in the ensuing years, something that Jobs would never have done.

That shift, I think, is what most clearly marks Cook’s Apple and differentiates it from the previous regime. Where Steve Jobs would interrupt a vacation to stand on a stage and insist that the poorly-designed iPhone 4 was no worse than other smartphones when it came to interference—an outright lie—Mr. Cook correctly takes the blame when his Apple makes mistakes. Someone like Forstall, who built his career both emulating and toadying to Mr. Jobs, was never going to make it under Tim Cook. And it was interesting getting the perspective of other executives on Forstall’s departure.

Looked at more broadly, Kahney provides an excellent rundown of Tim Cook’s life, both before and during his tenure at Apple. And while I skimmed through the opening chapters about his childhood and times at IBM and Compaq, the bulk of the book focuses on Apple and, most crucially, the time since Steve Jobs’ passing. One of the final chapters, regarding Apple’s future, is interesting, though it seems like the firm’s autonomous car efforts have stalled and changed dramatically since their inception. But it is Kahney’s belief that Cook, despite following one of the most iconic leaders in Silicon Valley history, has somehow emerged as Apple’s best CEO that will trigger the most debate. Kahney argues that logistics, not products, matter most at a company like Apple. And if that’s true, sure, then Mr. Cook comes out on top.

“Steve Jobs was never really a CEO,” one source told Kahney, in a hard-hitting bit of history-rewriting, given how decisively Jobs led Apple away from bankruptcy and then engineered the most stunning comeback in corporate history. But there is some truth to the notion that, once Apple became enormously successful and distributed, it needed a different kind of leader. Someone less mercurial and touchy. Someone, well, like Tim Cook.

I’m not ready to concede that Cook is a genius in the Silicon Valley visionary or engineer sense, and I’m still uncomfortable with the notion that he is a better CEO than Steve Jobs. But he is a better human being, for sure. And he is the better CEO for today’s Apple. And if you’re interested in a great overview of Tim’s still-ongoing tenure at Apple, Leander Kahney’s latest book is exactly what you need.

Tim Cook: The Genius Who Took Apple to the Next Level by Leander Kahney can now be preordered and will be available on April 16. I highly recommend it.

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