PhD's are notoriously (and understandably) finicky about doing non-research work when the job is sold as research, that's why you have to be sure you really need them. That issue has been around since long before data science in SaaS companies was a thing, it's been around since before the internet was a thing.
Assuming that there really is an exodus problem, PhDs being unprepared to lead teams and do non-data-science work is one theory that seems reasonable, but it definitely isn't covering all possibilities.
Having been in a couple of companies hiring data scientists recently, I personally think the big problem is expectation for data science in general, more than who's been hired to do the job. The couple of companies I've worked with, anecdotally, seem to expect "data science" to uncover huge missing profits, expose gaping inefficiencies, and reveal new revenue streams the business people didn't see. And when there turns out to be only minor ways to streamline things, the team of data scientists need something else to do.