Its largely flair and enviromentally based. Many combat systems are similar and only vary down to flair, if it works they should all look the same or highly similar due to coming to the same conclsuons independently.
The sibject on culture and how it impacts martial arts can be a life long pursuit into research anyway and i am sure plenty of socologists have looked into it, but i can only really comment on kicking hisotrically in England.
As far as i know for the (late)victorian peroid, kicking was looked down upon, if you were to kick you were seen as not a functional memeber of society (i forget the best words to put there) so that influnced the usage of boxing, fights were also seen as somethign you should do 1:1 as well. Now something amusing, i have seen some news articles from the 1800's during the savate vs boxing stage of the peroid where people would look at the fancy savate kicks and basically come to the conclusion they are useless or sub par due to the gymanstic ability needed to use them as opposed to punching somone in the face. And some people didnt hold that view obviously. So the argument about the fancy high kicks is a pretty old argument that can be dated to i think the 1800's at least.
This is not getting into say, the civilising of boxing and making it a gloved sport thus if everyone did boxing gloved their street fighting would be based on a gloved system as opposed to say if you took a culture that had a ungloved system in such persiverience. Or if it was common to solve your disputes via swords. Diffrent coutnries regulated dueling diffrent and had it banned or unbanned. Like the civilising of boxing started when i think someone had their freind die in it, so they pushed for a universal set of rules to hold matches to and that expanded into modern boxing. It basicallt got more and more icivl and more and more rules until it basically became modern boxing with the gloves and the ring.
And you brought up karate, as far as i recall in the kingdom karate was made in martial practise was banned for a peroid? Or at least restricted to a certain class so that brings up a diffrent set of circumstances to somewhere where it wasnt class restricted or banned. Then you have how judicial duels are done and their rules, if you only duel you could get good at some really obscure ruleset that doesnt reflect outside of the rules fighting.
Anyway, i could ramble about this all day if i wanted to, i think that got my point across. The U.K took a pretty moral right turn in either themid-late 1700's or early 1800's if i recall. Which largely led to the way the empire was managed and how the empire would be managed, instead of say putting the entire population of a colony into slave labour until they all die being the norm. I think there is a fancy name for the peroid but i think it cropped up either early Victorian or late Georgian.
Addendum: Obviously weapons that are avalible is a pretty big impact on how you fight, although its not always obvious. you may think a weapon with a good point would be used for thrusting yet this populace may have used it for cutting. There are usually many diffrent systems within a population denoting diffrences in goal and weapons being used. And there are always diffrences in opinion in what is and is not acceptable behvaiour. Thought i best make the addendum and cover my bases in case.