The scientific innovation in Natural Language Processing (NLP) and more broadly in artificial intelligence (AI) is at its fastest pace to date. As large language models (LLMs) unleash a new era of automation, important debates emerge regarding the benefits and risks of their development, deployment and use. Currently, these debates have been dominated by often polarized narratives mainly led by the AI Safety and AI Ethics movements. This polarization, often amplified by social media, is swaying political agendas on AI regulation and governance and posing issues of regulatory capture. Capture occurs when the regulator advances the interests of the industry it is supposed to regulate, or of special interest groups rather than pursuing the general public interest. Meanwhile in NLP research, attention has been increasingly paid to the discussion of regulating risks and harms. This often happens without systematic methodologies or sufficient rooting in the disciplines that inspire an extended scope of NLP research, jeopardizing the scientific integrity of these endeavors. Regulation studies are a rich source of knowledge on how to systematically deal with risk and uncertainty, as well as with scientific evidence, to evaluate and compare regulatory options. This resource has largely remained untapped so far. In this paper, we argue how NLP research on these topics can benefit from proximity to regulatory studies and adjacent fields. We do so by discussing basic tenets of regulation, and risk and uncertainty, and by highlighting the shortcomings of current NLP discussions dealing with risk assessment. Finally, we advocate for the development of a new multidisciplinary research space on regulation and NLP (RegNLP), focused on connecting scientific knowledge to regulatory processes based on systematic methodologies.