What is the reasoning behind the publication of poems in academic journals?
Your first reference comes from Qualitative Inquiry journal, that describes themselves as:


  Qualitative Inquiry (QI) provides an interdisciplinary forum for qualitative methodology and related issues in the human sciences. The journal publishes open-peer reviewed research articles that experiment with manuscript form and content, and focus on methodological issues raised by qualitative research rather than the content or results of the research. QI also addresses advances in specific methodological strategies or techniques.


Emphasis is mine. It seems that publishing poem in that case comments on the fact that insomnia affects general academic performance. That is an "experiment with manuscript form" that addresses statistics of insomnia.

Your second reference comes from "Women &amp; Performance: a journal of feminist theory" which aims to publish:


  scholarly essays from interdisciplinary feminist perspectives. For us, “women” and “performance” denote not simply what we study but how we study it—that is, not preconceived objects of analysis, but rather an open assembly of political, ethical, and aesthetic orientations, feminism chief among them. We encourage dialogues among various fields of performance scholarship, including theater and performance studies, dance studies, music history and criticism, ethnography, new and digital media, cinema studies, and cultural studies; as well as queer, critical race, and post- and decolonial theory. Working with/in this disciplinary hybridity, we explore critiques of gender, race, ethnicity, class, sexuality, dis/ability, technology, nation, and capitalism.


Emphasis is mine. That poem seems to connect work of the artists and current events, put work of artists into context. But that is just an opinion.

The shorter answer TL;DR would be that these poems represent unconventional (for Science/Nature/Cell readers) opinion pieces.