I believe there was no single factor, but rather a series of them which held various degrees of influence.

Most of the fantasy genre and media are defined by the influence Medievalism had on them, rather than Medieval studies proper. That means "the idea of a fabled past", rather than actual, researched context, both theoretical and material. It can be safe to assume that this kind of influence on said media stems mostly from the Romantic era, from the first quarter of the XIX century, which brought with itself a shift in the perception of the Middle Ages when compared with the previous tendency of the Enlightenment and XVII century.
It did happen that the Medieval period became a place where ethics and myths had found concrete shape, where national identities could be researched (and, mostly, hand-crafted) and the sense of belonging and origin could be nurtured and used in politics and cultural expressions. In such an occasion, the Nibelungenlied was conceived as: «[...] a sort of German Iliad, depicting the exodus of the German nation"»^(1) within the greater effort in turning the Dark Ages in a sort of gilded era, a different time where to flee when wishing to immerse in the fantastical and fabled.

Since medieval historical studies were not as developed in these years, and archaeology had a greater focus on Classical topics (titanic names of Greek studies such as Johann Gustav Droysen, Karl Julius Beloch and Karl Otfried Müller start their works and lives during the 1800s), the understanding of the material history and culture of the Middle Ages was much less reliable than it would be some sxty years into the XX century. Later examples of protections and weapons like XVI century plate armours, polearms and longswords would have been much more abundant than other surviving artefacts which could be linked to previous centuries. It is more common, as you've noticed, to mix dates and equipments without much consideration for what is being mixed, possibly without even considering the possibility of a mismatch mostly due to poor consideration of proper historical consults and/or budget constraints.

Additionally, I believe that the 1400s and 1500s exert a greater attraction for drama and fiction because of the historiographical myth of the Renaissance as the era of violence, intrigue and ruthlessness. Think about the TV series on the Medici and Borgia families, or that hideous show Da Vinci's Demons, along with the poorly understood and much demonized Machiavelli. Game of Thrones fits this mold the best.

Paradoxically, the late Middle Ages were a moment when the factors mostly associated with it (castle lordships, vassallatic service, holy wars, enclosed economies, etc.) had either changed deeply or disappeared entirely. When Tywin Lannister and Robb Stark yell "raise the bannermen" in a XVI century society by customs and dresses, would have received a big, fat "f**k you" when requesting their retainers to go to war for free, when it had become standard hiring soldiers and even one's own knights behind a regular contract and salary. This, by the way, was gotten right when Stannis Baratheon raises an army of his vassals through money he borrowed from the Golden Bank (another very common practice for kings from the 1300s onwards).

Lastly, I believe that some settings were conceived as set in a hypothetical "middle period", but then got adapted in TV or movie format and were "injected" a visual representation more fitting of the general expectation we might have constructed through exposure to previous media (let's take for example Gary Gygax's Dungeons & Dragons). The Lord of the Rings, I am rather certain, was invented as a land more akin to a X-XI century Northern Europe when Tolkien first wrote it, and was partially "dressed" in the later fashions when it became the astounding movie series we all know. Although, to be fair, some aspects of it still remained doused in that "Early Middle Ages vibe" it might have had at its inception with the way Rohan warriors look (very Saxon inspired).

I hope this helps you. Feel free to ask more as it is a very interesting topic.

Sources:

1. Di Carpegna Falconieri, Tommaso. "Medioevo Militante. La politica di oggi alle prese con barbari e crociati", Einaudi, Torino, 2011;

Contamine, Philippe. "War in the Middle Ages". (Italian edition). Il Mulino, 2014.

I thought most fantasy was set in the high middle ages mostly? Fantasy writing is a mosaic of smashed things from any period of european history, at the choice of the author's creativity.

In that sense denouncing The Witcher as anachronistic is a bit misleading, most fantasy works are anachronistic beyond belief, there's mythical creatures originated from celtic, germanic folklore smashed in something that closely resembles the french or the english high middle ages, and also literacy rates are high even among the poorest possible farmers, remember that writing fantasy is writing, most stuff is just whatever the author choose to put in their stories and just roll with it as if nothing was going on. Also now thinking of it, a lot of castles are built inspired on 19th century revival architecture, or not, it depends on the author for how it goes. Sometimes they're so anachronistic even for the contemporary perceptions of common sense, where else than in a videogame a poor farmer with malnutrition and a wooden club is a 1:1 match to a professional soldier wielding 17th century weaponry?

This goes back to your examples of late medieval weapons. Perhaps this sort of military equipment is more popular among authors / it captured the imaginary of the common folk better? For practical purposes (and marketing purposes) the history of warfare and society have been much simplified in fantasy writings, on one side to not make it too massive a text for the readers to digest, on the other because authors usually do little research on medieval history and just roll with what they know/perceive as factoid about the european middle ages, also it's often simplified to be more recognisable for what people are used, people's own biases and dumbing downusually a lot of how the power structures are organised/society behaves is inspired on medieval western europe of earlier centuries than that of late middle ages, some coming from the early middle ages others from the high middle ages, technologically too.

I think giving many examples of late middle ages centric games might be useful in this context, I don't consume much fantasy content admittedly, but most of it now thinking of it is high middle ages if not earlier, LotR, The Witcher (in a sense), Eragon, Skyrim, my guess is Zelda too but I'm not well informed enough, Dark Souls, GoT, Merlin stories - which reminds me, a lot of modern fantasy are just a direct inspiration from English stories (fictional or not), and some French stories (which goes back to relating to England often), and notably germanic folklore, be it because fantasy is an english genre, and be it because the english world being the center of modern western culture they can easily influence other western european societies. The Arthurian Legend, Beowulf, Tolkien's works, The War of the Roses, Robin Hood, even inspirations from other european cultures are anglo-centric, The Hundred Years War, The Norman Conquest of England, Viking Age (but only its relation with England, not with itself or with other cultures). You can essentially break down contemporary fantasy writing into these eight components with 99% purity. Which goes back to another matter, Fantasy is very centered on european history, and within european history, western european, within weurope, France and specially England are the main component of these stories