The natural conclusion to this argument is that everyone on earth is speaking the same language, because they all descended from the Mitochondrial Eve’s utterances 150000 years ago.
(Tangent -- certainly not all languages are descended from a hypothetical Proto-World, since we have examples of brand new languages forming: any creole languages, or Nicaraguan Sign Language. Whether most of the major language families are descended from a Proto-World is very much an open question, and probably one that will never be answered, since even if say, English and Navajo are genetically related, they diverged so long before we had written records that no trace remains.)
In any case, there's a meaningful difference between a language gradually changing over hundreds of years such that the newer varieties are quite different from the old ones, and a language truly dying, because it has exactly one remaining native speaker, and that person dies.
It's a question that linguists (who are scientists) strive to answer in ways that are useful to studying, reasoning about, and explaining language. It's not much different than the species problem in biology. Everyone knows that speciation happens gradually, but scientists still propose ways of defining and explaining speciation to aid in scientific inquiry. The labels and dividing lines themselves are not empirically observed, of course, but that doesn't mean they're unscientific or outside the purview of scientific inquiry.
I would be very surprised if such a thing exists.
Sure they are, although a debate wouldn't be contained in one paper written collaboratively by debating authors, as you seem to imagine -- it would play out over a series of papers, each of which cites previous papers and claims they're wrong.
For example, Timm 1989[1] argues that modern Breton is a VSO language, disputing the claims of Varin 1979[2], who claims it is SVO, which in turn disputes the traditional understanding that it is indeed VSO.
Or the famous paper of Haspelmath 2011[3] citing many other authors' proposed approaches to word segmentation and arguing that they're all wrong (i.e., that "word" is not a meaningfully defined concept in linguistics).
Where are the papers that you claim exist about the lines between languages? If this is really something mainstream linguists care about, you should be able to give examples in non-fringe journals.
I just checked the citations on the Wikipedia article for Middle English like you suggested, and found zero papers about whether Middle English should be considered "the same language" as modern English. Can you tell me which ones specifically you mean?
[1]: Timm, L. (1989). "Word Order in 20th Century Breton". Natural Language & Linguistic Theory, Vol. 7, No. 3, Special Celtic Issue, pp. 361-378 (https://sci-hub.tw/10.2307/4047723)
[2]: Varin, A. (1979). "VSO and SVO Order in Breton". Archivum Linguisticum 10, pp. 83-101
[3]: Haspelmath, M. (2011). The indeterminacy of word segmentation and the nature of morphology and syntax. Folia Linguistica, 45(1). (https://sci-hub.tw/https://doi.org/10.1515/flin.2011.002)