Shakespeare made Mercutio so sparkling and diverting that he had to kill him in order to allow the tragic focus of the play to emerge. Do you agree?
I think that is a very interesting idea, although I can't say that I exactly agree with it. It seems to suggest that Shakespeare was in the habit of writing his plays without knowing where he was going with his plots or characters. It seems pretty radical for an author to create a character and then decide to kill him just because he was getting to be too engaging and interesting. I would suggest as an alternative theory that Shakespeare intentionally made Mercutio, as you say, so "sparkling and diverting" just because his death would add to the "tragic focus" of the play. In other words, he created him with the intention of killing him; it didn't just suddenly occur to Shakespeare that Mercutio was stealing the show and that he had to kill him off.
The only parallel that occurs to me offhand at the moment (although there must be many others in world literature) is in the short story "The Monkey's Paw" by W. W. Jacobs. Herbert White is always happy, funny, carefree, full of life. Then when he gets killed in a factory accident, the parents seem to suffer more deeply from the loss of this young man who was the light of their lives, and their little house without him seems all the more gloomy. The author deliberately made Herbert lighthearted, witty, lively, and likable because he intended to kill him off.
Still, I find your theory about Shakespeare having to kill Mercutio intriguing because of what it seems to suggest about the way Shakespeare worked on his plays.