Pick any field. Find some measure of who pushes the boundaries the most in that field. Check after picking the metric, not before, what percent of those making the advances had a PhD, compared to the field overall.
For example, in computer science a the top advances sometimes get a Turing Award. Turing Awards winners need not have a PhD. Most people working in computer science don't have PhDs, yet among Turing Award winners, 59 have one and 13 don't (and most of those have masters degrees).
The same happens in chemistry, physics, biology, engineering, history, geology, psychology, and on and on.
Maybe a PhD is more than a "fake status indicator"? Maybe those most driven to push boundaries very often get a PhD along the way to become more skilled in their field.
Care to present a field and a metric of who has pushed the boundaries the most for which we can asses the impact of PhD and non-PhDs where PhDs are not the most impactful?