I've heard and observed that the Ph.D teaches you one crucial skill - how to take a vaguely defined research problem that nobody has done before, where you're not even sure that a solution exists, and make tangible, rigorous progress on it. Your actual doctoral topic as a Ph.D student will probably be useless. Most of your coursework is the same as what any master's degree gives you. But the experience that sets you apart from B.S. and M.S. graduates is that of slogging through a dissertation, trying to make an original contribution to knowledge.
There are other ways to develop this skillset. Founding a company does it as well, as does developing a new product from scratch. High-level creative work (eg. writing a novel, getting traction for your band, producing a theatrical performance or radio show) does as well. Companies love to hire candidates from these backgrounds as well, but most don't want to work for someone else. (Interestingly, depression and anxiety might actually be a feature of developing this skillset, not a bug - these two mental disorders are endemic among these fields as well.)
The reason employers get hung up on this is because the economic returns to innovation are at an all-time high these days, and so developing that blockbuster new product or highly-efficient new process makes a lot of money. And part of the reason returns to innovation are so high is because so few people are actually innovating. While there certainly exist people with just a bachelors or even no degree at all who are capable of innovating, a large number of bachelor's holders do not have the toolset or mental fortitude to break out beyond what everybody else knows and create new knowledge.