I have read a lot about why most statistical packages do not report the significance test results of random effects (e.g. here) Is there any publication about this precise topic that I could use to cite this in my paper?
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To my knowledge, the most thorough discussion of this is Doug Bates' mailing list post from quite a while ago. There's a nice summary of this on the GLMM faq: https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#why-doesnt-lme4-display-denominator-degrees-of-freedomp-values-what-other-options-do-i-have
It largely boils down to no one knowing quite how to calculate how many parameters are in these kinds of models. If you don't know how many parameters there are, then you also can't calculate a degrees of freedom, and hence, can't get a p-value.
If you need something to cite, there's a Bolker et al paper in Trends in Ecology and Evolution you could cite:
http://www.poulsenlabduke.com/uploads/1/9/3/6/19363955/bolker_et_al._2009_tree.pdf
