The example of Burgundy is long after the middle ages have ended. Has Charles the Bold been a medieval duke, first of all he would not have been able to amass that much land (and control it effectively); secondly he would have sought to be elected emperor instead of trying to have a royal title "invented" for himself. Not comparable. Charles the Bold wanted to be recognized as an independent and legitimate ruler of his territories, as a territorial lord in the early modern fashion who rules his lands directly. He did not want to become a king in the feudal sense, where he would have lords of his realm, and a bunch of dukes ruling his lands for him. Not medieval.
Depends when one considers the end of the Middle ages. If one considers the fall of Constantinople as such the Hundred Year's War was already on and Burgundy was a large and powerful duchy, seeking independence from its liege. Seeking a crown after securing such independence de jure would be the logical next step and actions of the later Burgundian dukes fallowed the inertia of their Medieval actions.
But what is the Corsican example supposed to show? That medieval rulers went to great lengths to be formally recognized as kings, even when their actual power was already on par with that of a king? If so, then Corsica is actually a bad example, since IIRC it was only made into a kingdom (by the Pope) in order to legitimize the rule of the Aragonese King over those lands. He was already king, the whole point of the exercise was to legitimize his rule over the islands. (The islanders hated him.) An independent ruler of Corsica or Sardinia would definitely not have sought or been granted a king title from the pope.
The kingdom of Sardinia and Corsica was made to counterweight the kingdom of Naples, so Aragon still getting a crow out of the whole thing. And even such paper kingdom was of value 400 years later. Internationally recognised, or at least such recognised by the at lest theoretical power brokers, is important and valuable.
He could always have elevated himself to be king of the island, which would be perfectly o.k. by medieval logic, since the island was outside the recognized jurisdiction of the established kingdoms at the time. (Until the pope created the crown of Corsica and handed it to the Aragonese, that is.)
I would disagree with you there. According to the medieval logic if one proclaimed himself king, it had no value outside of his own court and may not even be recognised fully within his own state. The kingdom on Earth was a shadow of the kingdom of Heaven, as the kingdom of Heaven was ruled by Jesus, so a kingdom on Earth was ruled by a king, in some sense chosen by by God and to some extent a representative of divine powers on earth. For obvious reason such recognition was not given lightly by the already existing powers, and those already having such recognition would rather not expand their numbers. Sardinia was a kingdom because the vicarius dei said so and cannot come into existence because a temporal ruler may want it to. The only temporal rulers that can also say so are the Roman emperors in the east and west.
There were lots of rulers of fringe territories who were called "kings" in medieval times, but their titles were worthless. For example the leaders of small pagan tribes in remote regions could be called "rex Pruthenorum". But no medieval Christian ruler in his right mind would waste efforts on seizing that land just for the titular ownership.
Pagan rulers can call themselves whatever they like, and be called by anybody whatever they like. “Rex Pruthenorum” was not a title granted to the pagans by the church or by the Roman emperor, thus it had no value. The family of Christian rulers was an already established concept in the Early Medieval times. To be king means to be recognised as such by your peers or your “betters”. No medieval Christian ruler in his right mind would waste efforts on seizing that land to claim a title, because there was no title to be claimed. One had to create one, bring the land and the people to the Christian universe so to speak.
"Might makes right" was the slogan of the middle ages, also "strength creates respect". Not "fancy titles create respect". That would be a renaissance / baroque meme.
Again I disagree. “Might makes right” is a gross misinterpretation and understatement of the most burdened by cosmology, tradition and symbolics era in the history of Europe. Might always had to come dressed in some kind of reason, which was fitting the world view of the medieval man, if no amount of might made it right, at least at the table of international politics. The pope claimed dominion over temporal lords, not because he was a third party that could be extremely useful in a pinch, but because he was a successor of Peter and had received the Constantine's gift. Th Fourth crusade took Constantinople not because they were able to, but because the were descendent from Trojans. No mater how ridiculous was such claim or that it came after the fact it was always there in the Medieval age. Its veracity might be proven by steel, but you cannot expand just because you are able to, you cannot just claim to be king without being recognised by some divine right. At least not without all available Christian rulers gunning for your stuff. “Might makes right” is also fitting for every day and age, in most of the Modernity it was covered by wrapping of the balance of power, in the Medieval age it was covered by the concept of the family of Christian rulers.