The current wave of digital transformation has spurred digitisation reforms and has led to prodigious development of AI & NLP systems, with several of them entering the public domain. There is a perception that these systems have a non trivial impact on society but there is a dearth of literature in critical AI exploring what kinds of systems exist and how do they operate. This paper constructs a broad taxonomy of NLP systems which impact or are impacted by the ``public'' and provides a concrete analyses via various instrumental and normative lenses on the socio-technical nature of these systems. This paper categorises thirty examples of these systems into seven families, namely; finance, customer service, policy making, education, healthcare, law, and security, based on their public use cases. It then critically analyses these applications, first the priors and assumptions they are based on, then their mechanisms, possible methods of data collection, the models and error functions used, etc. This paper further delves into exploring the socio-economic and political contexts in which these families of systems are generally used and their potential impact on the same, and the function creep of these systems. It provides commentary on the potential long-term downstream impact of these systems on communities which use them. Aside from providing a birds eye view of what exists our in depth analysis provides insights on what is lacking in the current discourse on NLP in particular and critical AI in general, proposes additions to the current framework of analysis, provides recommendations future research direction, and highlights the need to importance of exploring the social in this socio-technical system.