I can't answer why it wasn't done more often, difficult to say why exactly. But Henry VII first son, Henry VIII's older brother and Catherine of Aragon's first husband, was called Prince Arthur. He was meant to be the first king Arthur. Which has been suggested to have been an intentional Arthurian reference.
But perhaps the reason it was not more common was because Arthurian legend originated with the Celtic Britons, particularly in Wales, Cornwall and Brittany where Celtic culture remained, so it might be seen as a bit revolutionary to an Anglo-Norman dynasty. There was a rather threatening legend about King Arthur returning to protect his people and reclaim his throne that was popular with Celtic peoples.
It's noteworthy that Henry VII had native Welsh blood on his father's side and was raised in Wales, so perhaps he had a slightly more personal, comfortable relationship with the story. In the same way he used the Welsh Red Dragon and his suggested descent from a famous Welsh historical figure to raise support when he landed on the west coast in Wales, before Bosworth.
When princes are born, a great deal of care is taken over their names, and upon how those names invoke or respect the past.
Children born higher in the line of succession tend to be given more "kingly" names. But circumstances are rarely predictable, and there are several events where a son has been groomed for kingship, but died before they inherited.
Take Arthur of Brittany (b. 1187) for example. Obviously, he didn't become king. But at the time of his birth, during the reign of Henry II was in a direct line to succeed the throne of England (Richard was next-in-line, but without any legitimate children, Arthur's father was the 2nd) . When John was born, however, he was the 5th son. The chances of this baby ever becoming king were, at time of birth, slim.
Its also worth noting that when we apply regnal numbers to the names of kings from the Conqueror until Henry III, then we have retroactively applied that number. They were not known in their time as "Henry I". They were kown by their cognomen. So, William was often known as "The Conqueror", but styled himself as "The Bastard". (The medieval monarchy was a lot lot less formal). It wasn't until Edward I that kings started adopting a number in their time. So, while modern historians would refer to "Henry I" or "Henry II" for clarity... there is no need to do this for John. (Stephen, and Anne also. Incidentally, they were also all but overthrown after a civil war)
As for the reasons why there has never been another king named John? Its because fairly or unfairly, John's reign has gone down in history as a byword for bad kingship. As a king, he's best remembered as the villain of Robin Hood, and that is simply not the kind of image anyone wants to conjure up. Better, to invoke the regal majesty of a "William" or a "George". It doesn't particularly matter whether these common imaginations of past kings is justified or not. The imaginations exist, and when a baby is being set up to be a future king, its important to consider how these cosmetic details will be interpreted by the public. After all, that's ultimately what a monarch is, a PR exercise.
I can think of a few main reasons,
It is worth noting that there is an obvious exception to the above. Henry VII had a son Arthur who was his heir. The name was chosen intentionally. The Tudors had Welsh ancestry, so playing up the Arthurian connection made more sense for them. But, Arthur dies and his brother Henry VIII doesn’t seem to continue with the Arthurian illusions. He probably associated the entire thing with his dead brother.
By the time of the Stuarts a century later it does seem the Arthurian legend had been substantially changed. For example, in the Opera called King Arthur by Henry Purcell the story is significantly altered. Many of the fantastical elements we consider key components of the myth we know today are left out. The Opera also includes a lot of references to pre-Christian Britain and Norse/Roman religion, so if that was the popular view of Arthur by that time, as a figure representing an archaic age, it probably wouldn’t make sense to use his name. Keep in mind regardless of a given English monarch’s religious views (they varied quite a bit) as religion became the hot button issue it was in the 17th century associating yourself with a story with many pre-Christian elements may not have been desirable.
Hey there,
Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.
If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!