For example, Brian Sooy holds an Associate's Degree from Lorain County Community College, and a BFA in Graphic Design from Bowling Green State University.
I chose graphic design because I love type and solving problems with all the resources a designer has at his disposal. plus design is the perfect blend of aesthetics, technology and problem-solving.
For example: what I've seen in 25 years of design experience is that an individual with a masters in design may approach a design problem too academically (over-thinking it, or suggesting a solution that is so esoteric that the client immediately says "huh?").
Or, they may suggest a visual design solution that they think is valid based on their educational experience, but is totally foreign, inappropriate, or not suitable to the audience and/or client. Sometimes it's as simple as setting a typeface too small, rendering it unreadable.
Design for design's sake isn't always suitable with regard to design for business.
I think designers need more understanding of how businesses work, what the role of design is in the business process, and how to run a business.
Not that a master's degree is invaluable, more education never is.
As to the critical thinking: that should be emphasized in the undergraduate studies even more, but if a designer wants to be considered a consultant, (which we are), then certainly a master's degree would be valuable for that as well.
Not only do you need to understand how to solve problems (the essence of design) you need to understand a world of software, file formats and digital processes.
Of course you will need software skills to have a career in graphic design, but those are acquired skills that anyone can learn. Of more importance is the ability to think critically about the design problem at hand, then combine your design skills with your technical knowledge to find the solution.
Have you heard of the rumored new program that will combine the best of Illustrator and Macromedia FreeHand? It will be called Adobe Frustrator. (groan!)