An interesting question, I think! So first of all, the collective nouns you're talking about are known as 'terms of venery'. 'Venery' comes ultimately from French, and means 'hunting', as in the sport of the chase of wild animals for game. The fact that it comes from French is important. After 1066, England's Anglo-Saxon Germanic-tongued past hybridized with its new aristocrats, the Norman French. The interaction of these languages is not a pure dualism, but a dialogue of mutual growth, and although English today is considered the descendent of Old English, the Germanic tongue of the Anglo-Saxons, it has a huge imprint from the Norman conquest and the forms of French they brought. Although there is evidence that, by the 1300s, the children of Anglo-Norman nobility learned English before they learned French, they were nonetheless taught French as an absolute necessity, as the courtly language, and often the administrative one.

It may be said that for some very specific groups of people, hunting was a form of subsistence and a source of basic nutrition. For most, however, I think it's fair to say that the social and sporting functions were more important than obtaining food, and hunting as an institution (rather than hunting as an act of foraging) was heavily associated with the aristocratic and royal classes. The Norman conquest reinforced a trend that had already begun, with forestry laws intensifying the restrictions on hunting for common folk and heightening its status as a lordly pursuit. I think it can be said of courtly life in the English middle ages that it was in a big way concerned with playing roles, with individuals aiming to conform to archetypes in order to gain status and live up to the status society nominally accorded them. For younger men and boys, hunting was training and a precursor to warfare, but it also created opportunity for social networking and for the young men of great houses to be compared to one another by their rivalling seniors, for transgenerational alliances to be cemented, and for intrigue.

Prowess in hunting was therefore not merely about the martial archetype therefore - loosing your arrows straight or having a good arm with the spear - but about fulfilling the social archetype as well. Like with any specialized subject, to be considered competent you not only had to walk the walk but also talk the talk, which means knowing the jargon. Jargon is not an insulting or derisive word for the language they used, by the way. Jargon is a technical description, being the words used by experts to establish their expertise. Jargon is esoteric, which means it is only known to the initiated. An imitator would be caught out by their incorrect usage, even spurned or mocked, and they would be considered an outsider. In this way, it acts as a Shibboleth. Terms of venery had their origin within Norman French hunting traditions, and it seems that during the centuries following the Norman invasion the terminology for hunting deepened and became more complex. They were surely not the only thing one needed to know the terminology for in regards to hunting, but they obviously have had a particular staying power that has transcended their original case use and become generalised to English vernacular usage. We can see in the Boke of Seynt Albans, printed first in 1486, essays on the subjects of hawking and hunting with a view to compiling what was considered necessary knowledge of these pursuits for a gentleman. In this book, many terms of venery are listed, and I have heard the modern popular persistence of the most common of these terms (gaggle of geese, murder of crows etc) attributed to this book. Regardless, whether this book did secure their posterity or not, the Boke of Seynt Albans also gives us a hint that by the late 15th century these terms had become so emblematic of hunting as a lordly sport that they provided the format for the usage of analogous terms outside the world of hunting, with examples in the book of collective nouns for types of people, for example: 'a subtlety of sergeants' (which, by the way, refers to lawyers and not military officers). This kind of usage is very clearly playful and humorous, and shows that what had begun as a technical vocabulary had clearly gained vernacular currency as a trope.

This is where we leave pure consideration of evidence and I offer an original opinion, but I suspect this last point about the ludic qualities of the formula explains in a large way its persistence. People clearly relish discovering archaic terms of venery. I have on multiple occasions had acquaintances quiz me, for example: "Do you know what the collective term for [for example] unicorns is?" (Apparently it's a 'blessing' - I have no evidence for this being true though). People equally enjoy conjuring their own made-up collective nouns when they don't know or one doesn't exist. So, I would summarise by noting the mediaeval origins of the formula as a useful if arcane technical jargon, and then emphasise how the formula has grown beyond this specific origin to be a word game that is easily played across the centuries by innovators in our fascinating language, with some famous examples having been particularly helped by their repeated use in literature through the ages.