I think I might just be used to the current title, but I think the other one sounds weird. If it were reversed I'd likely be saying the same thing. It's all about what we are used to. This is true for pretty much any context, not just movie titles.
The Lion King does focus on one lion becoming the leader but it should not have been called the King of the Jungle. It was a more personal story of one lion growing into his own and becoming a man which relates to a lion king. If it was more about the lion leading the whole state than King of Jungle would have been a better name.
I think the title "The Lion King" was perfect, wouldn't change a thing. It was a different way of saying the cliched "King of the Jungle". The Lion King is still one of my favorite movies of all time. I love every bit of it, wouldn't change a thing, including the title.
"The Lion King" is a fitting title for the movie rather than "King of the Jungle". The former title refers to the fact the movie is based on a lion who is king, whereas the latter title refers to lions as king of the jungle. While lions are in fact often considered Kings of the Jungle, that is not what the movie is trying to portray.