Great question! On mobile so this might be a bit more tearse than I'd like. Not a historian but grew up fascinated by the tales of King Arthur, Robin Hood, and study as much as I could on that period in high school and college, going as far as to major in anthropology and history but have not worked professionally in that field.

To start, let's just say the romanticism of the medieval period actually starts in the medieval period itself. Fantasy elements mostly have their roots there as well and what we see throughout generations of literary publications are trends where fantasy and the romanticising of the medieval period wanes and waxes. Favored during the middle ages, out of favor during the rennaissance and pretty much not around again until the mod 1800s.

The legends of King Arthur are perhaps some of the most important in establishing our current fantasy medieval genre as it would be very difficult to paint a modern fantasy novel, tropes and all, set in the medieval period without acknowledging the impact Arthurian legends and their publications have had throughout the centuries. Think: magic sword, child of mysterious birth, land divided - it's basically already a D&D campaign.

Stories about King Arthur begin with the first writings by a monk, Geoffrey Monmoth who starting writing down a tale of a British warrior who united several factions and defeated the Saxons (probably vikings). The story gets modified by several other monks in England and France in the 12th and 13th centuries where elemenys like Lancelot and Guineviere are added. The story really explodes with the printing press and starts to find common knowledge when it is more widely published again towards the end of the high middle ages in 1485 by sir Robert Mallorys Le Morte de Arthur, the same year the brutal War of the Roses comes to an end in England. Like Arthur who has no true born heir, the English Civil Wat started in 1456 because of similar reasons.. The themes of King Arthur, unity, loyalty, betrayal, chivalry, are all facets of the time where one can imagine a yearning for "one land one king."

The War of the Roses is also an important historical setting for fantasy literature, which aside from the political intrigue which fascinated George RR Martin to pen Game of Thrones, this was one of the last major conflicts prior to the age of gunpowder. While cannons did exist during this time, the setting is of knights in full steel plate, infantry were also very well armored and the weaponry required to get through all that were gruesome and menacing - Warhammer, two handed swords, heavy cross bows, maces, falchions. Men died in massive numbers and the country side was torn apart. It was a dark and uncertain time for England.

Chivalry, the concept is essentially a romanticized notion of what a knight should strive to be but it is mostly a fantasy. The code of chivalry itself being mostly an honor agreement put forth by the Pope which was sometimes adhered to be often ignored. Knights were to fight other knights with the goal of capture and ransom. If there was killing, it was largely done with the approval of the church, doing so otherwise was largely shunned, this doesn't mean it didnt happen.. The acts of brutality more or less get written off as flaws. King Henry V executing French knights taken prisoner at the battle of Agincourt comes to mind. Knights were privileged brutes that professionalized killing; but, the telling of King Arthur idealises them as protectors of the realm. In some ways Henry V embodies King Arthur, a flawed king, he unites a fragmented England, he brings his enemies to their knees and he dies tragically before his time.

Idealistic, flawed, heroes are a cornerstone of fantasy literature, be their ideals good or bad - look at Boramir(sp?) from Lord of the Rings. Boramir becomes a villain when he follows his chivalric ideals of protecting Gondor at all costs when he tries to take the ring from Frodo at the end of Tolkien's "the Fellowship of the Ring."

Other fantasy tropes, like the rogue impoverished noble living in the woods as an adventure and champion of the commoner come to light in 1375(I think?) with the first tellings of Robin Hood. Robin was an example of what could happen to corrupt nobility, echoing many ideas of the magna Carta (1216) despite its more modern interpretation on wealth distribution.

The trope of the cleric has a clear connection to preists blessing armies before battles, additionally, there were warrior priests who served monastic orders like the Turonic knights and Templars. There isn't a lot of literature romanticizing "battle monks" but what we know is of historical record, as particularly the Templars created and cultivated a mythology around themselves and their power as they became one of the most prominent banking and insurance providers of the time.

Wizards and witches have generally pertained to secular mystics living on the fringes of society. Perhaps during the middle ages this was anyone with wisdom that was outside or outlawed by Christianity. Merlin was more of the narrator in Monmoth's Arthur, a Welsh figure and madman retelling the tale of the British-Roman war leader but he takes a more magical, central figure when the French adapt the story. Knowledge such as medicine, astronomy, engineering, basic chemistry, were all around during Roman times, and were all largely absent outside church settings during medieval times. It is interesting that the wizard in Arthur's story is not of Christian roots but he is still allowed to present Arthur as a more or less Christian ordained king.

Another hugely influential book on fantasy is the Fairy Queen, 1590, written by Edmond Spencer during the reign of Queen Elizabeth. Fairy Queen is long and follows three knights who each embody something special, and in this case amongst the rise and importance of nationalism, that something is inherently British. A popular story is that of St. George and the Dragon (1985, Margeret Hodges) which adapted from the first part of the fairy queen saga which follows an adventurer known as the Redcrosse knight.

Not to ramble too much but as you see many of the fantasy tropes you find in modern literature have roots in romantic literature spanning the centuries. Whether it is art imitating life or visa versa there are very well connections of fabtasy elements to the events of the times in which they found popularity. It isn't hard then to insert modern problems in this more or less timeless setting and play them out.

Thanks for the lengthy reply. I'm across the majority of what you mention as I did a lot of medieval history at university. There was another question asked today which illustrates what I was getting at perhaps. Someone asked "were there adventurers in the middle ages" and defined what they meant more or less in terms of a Dungeons & Dragons quest party. A few days earlier someone asked "the dark lord in his dark tower is a common fantasy trope. Did medieval people see their enemies this way". Both of these seem daft to me - obviously Fantasy is Fantasy and history is history. It seems like the connection between the settings of fantasy novels, role playing games etc and Medieval Europe is being overstated in the popular imagination