Now that I think of it...
I think the reason why Sir Kay is always such a loudmouth and why he is always getting his ass kicked in the Romances is because it's a holdover of Flyting.
Flyting is an ancient practice of ritual insult dueling, found in a number of cultures, most notably Norse and Celtic. It involves two parties verbally sparring each other in poetic verse, often with provocations of cowardice and sexual deviancy. In other words, literal rap battles and diss tracks.
Presumably, as one of the oldest characters in the Arthurian Mythos and one rooted in the Welsh poetic tradition, Kay would have been expected to be not just a powerful warrior but also a combative wordsmith that can raise morale, praising allies and jeering opponents.
This comes into conflict when the High Medieval Period comes along and principles of Chivalry and Courtliness came into vogue. The philosophies of that time emphasized the cultivation of a well-mannered and sensible warrior-courtier, not starting needless conflicts amongst peers while maintaining martial hardiness.
The ability to brag and getting under a rival's skin probably ran counter to this new ideal of being a well-behaved knight, so steps had to be taken to curb and remove that culture from the warrior ethos.
And as a result, Kay becomes the punching bag for this push towards gentility. By presenting him as a boorish loudmouth that gets beaten up by other more courteous knights for said bad habit, it serves to enforce the idea that you don't want to be this kind of warrior and ought to practice keeping your mouth shut.










