The idea that universities should become entrepreneurial, commercialized, private commodities or should serve politicians and governmental agencies has been promoted by the university-industry-government relationship-based Triple Helix approach and is reality in many places. In contrast, a reemphasis on universities serving the public good has been demanded by proponents of transdisciplinary sustainability research. To better understand the tensions between public-good-oriented approaches of transdisciplinarity and entrepreneurial, market-oriented Triple Helix and third-mission approaches of science-practice collaboration, this paper takes a closer look at the history of universities' roles and functions. We then elucidate the practice of transdisciplinary processes and discuss the "science for and with society" approach of transdisciplinary sustainable transitioning. We argue that transdisciplinarity for producing groundbreaking sociotechnical solutions has to serve (a) the public good and (b) calls for independence, academic freedom, institutionalization, and proper funding schemes. Third-mission conceptions that follow the commercialization/capitalization of scientific knowledge are in conflict with the conception of science and of transdisciplinarity serving sustainable transitioning. The development of groundbreaking ideas for sustainable transitions must acknowledge the complexity and contextualization of real-world settings. Therefore, collaboration between practice and transdisciplinarity calls for the input and cooperation of authentic practitioners, i.e., the experts of practice and real wold complexity. The challenge of transdisciplinarity is to properly relate the fundamental expertise of practice to validated academic rigor. This implies that transdisciplinary research is a critical element of the university's research mission.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.