No research on this topic,-to my knowledge. In many professions there is a move away from the requirement for a credential-based degree since it is assumed that a measure of competency can be achieved in many other ways. For example, secondary education or even less plus experience plus alternative ways of learning the profession (mentoring, apprenticeship, etc.). I once knew a professional who, in place of a degree on her business card, had written "School of Hard Knocks"; touting the importance of her personal experience and learning. It is assumed of course that university-based degrees have a body of knowledge and specific skills related to the degree -as well as applied skills. The argument then becomes the level of competency required to practice in a specific profession and how one measures this competency. There are many ways to do this.Some professions have entry-to-practice exams but they are not competency-based nor do they predict how good you will be as as a practitioner within the profession . A good example of this is the Psychology Exam. To become a registered/licensed psychologist you must have either a master's level degree of doctoral level, depending on jurisdiction, plus you have to write an exam called the EPPP. This is a multiple choice exam. What does it measure other than you know specific knowledge or are good at taking multiple exams (test-taking intelligence)? Many people fail it first time round, yet, they are probably more competent in the profession than those who study hard (after receiving many degrees) and pass it on first go. Even though many pass it and become psychologists, we often know that someone with whom you have a good relationship, or someone with whom you develop a good relationship and who can really listen and hear you can be as effective or more so than a professional who does not have good people skills (yes, there are physicians and psychologists and psychiatrists, and...who do not have good people skills).

If you look at the question another way, sometimes (sometimes lots of times) incompetent people get degrees. Sometimes smart people act stupidly, etc. This situation occurs in all kinds of professions and workplaces.

I hope this helps.