Not the parent but the pro argument would be along the lines of a lot of people still assigning (a probably outsized) degree of credibility because you've written a book on a topic. And, secondarily, it does show you can take on and complete a significant project.

The con speaks to the other comment about selling. Writing a book takes a lot of time which could be spent on other things more directly related to building a business. (And the book itself probably won't make much money.) A website/blog with even a modest amount of good content may go almost as far as a book for a lot less time.

Don't get me wrong. Being published, especially through more credible publishers, can be good for one's career. I'm pretty sure it has for me. But, on the other hand, I haven't had to trade-off revenue vs. writing time.

That, and I have met a lot of interesting people who I would not have met otherwise.

I am a small fish in a small pond in my chosen career, but writing helps my own understanding. Explaining things helps understanding.