I assume that my question has close relations to linguistics and
archaeology as well, but I would like to know if there are any general
historical science theories about the widespread nature of languages.
This final paragraph is intriguing. I am not sure if historiography can be written without contribution from linguistics and archaeology. That would be ignoring important data of human history.
On MCW's reference (comments and answer, above) to "The Horse, The Wheel and Language" by David Anthony, this book is important precisely because it incorporates historical linguistics. David Anthony's defence of historical linguistics as a key element of archaeology, pp. 16-7, is a reminder of its relevance to historiography.
If we accept historical linguistics as part of "general historical science", the most persuasive answer would be "Farming-Language Dispersal hypothesis" (Wikipedia). Simply, population density from agriculture provided excellent conditions for prehistoric societies to disperse.
The Encyclopedia of Global Archaeology (2nd edition, 2020), also tells us that historical linguistics, although overlooked often, it should not. I suppose I am doing the same, in this answer. The entry at page 4176, on Farming-Language Dispersals: Principles:
Among various potential "window on our past," once rich seam of data
is all too often overlooked: the linguistic record. Above all, much of
the world so so dominated by just a handful of vast language lineages
as to cry out for explanation. That explanation, moreover, can only
lie in the same contexts and processes that humanity's cultural and
population (pre)history more widely. Indeed, of all attempt to account
for these broadest patterns in the linguistic panorama, one of the
most ambitious generalization is the "farming-language dispersals
hypothesis." Most simply put, this proposes that many of the most
significant language families - in both geographical range and speaker
numbers - dispersed with, and primarily thanks to, the spread of
In the case of Indo-European languages, it was genetic adaptation to milk tolerance of adult Yamnaya society, around 4000 BCE, that allowed the prehistoric migrations of Proto-Indo Europeans.
From the abstract of a recent article, Wilkin, S., Ventresca Miller, A., Fernandes, R. et al. Dairying enabled Early Bronze Age Yamnaya steppe expansions. Nature 598, 629–633 (2021) - https://doi.org/10.1038/s41586-021-03798-4
The rapid onset of ubiquitous dairying at a point in time when steppe
populations are known to have begun dispersing offers critical insight
into a key catalyst of steppe mobility. The identification of horse
milk proteins also indicates horse domestication by the Early Bronze
Age, which provides support for its role in steppe dispersals. Our
results point to a potential epicentre for horse domestication in the
Pontic–Caspian steppe by the third millennium bc, and offer strong
support for the notion that the novel exploitation of secondary animal
products was a key driver of the expansions of Eurasian steppe
pastoralists by the Early Bronze Age.
Finally, having said the above, I believe it should be more than a single-factor (agriculture or by-product of domesticated animals) that created the necessary conditions for successful disperses of so many ancestral languages. There has to be more factors that we have yet to identify. For instance, environmental conditions, in whatever form, could also have been a major contributor in some disperses. In this, I think I am supported by a very thorough and relevant book on this very topic, "Language Dispersal Beyond Farming" by Martine Robbeets & Alexander Savelyev (Max Planck Institute for the Science of Human History, Jena, 2017) - open access.