Quint, on the other hand, is an arrogant narcissist who gets himself killed, nearly gets the whole crew killed (and would have if not for Brody), and fails in his only mission, the one he bragged he was the only one that could do. He is, in the end, kinda pathetic. Which, if there is a point about masculinity in this movie, that may be it.
The ending in the book is a bit different. Quint and Hooper both die, and Brody only survives because the shark dies from the various wounds it received during the fishing trip. Spielberg didn't want such a gloomy ending, so he changed it up.
I think to really understand Jaws, we need to understand Moby Dick, and for that, we need to know what inspired Melville to write it. Like Quint's ordeal with the Indianapolis (a true story everybody should learn about!), a similar incident happened to a whaling ship out of Nantucket called the Essex. However, instead of Japanese torpedoes, the Essex was sunk by a whale. The Essex was captained by captain Pollard, who became Ahab, who then became Quint. What happened is that Pollard was out on longboats hunting whales when a sperm whale basically sunk his ship by ramming it twice, leaving Pollard and his crew stranded on the longboats in the middle of nowhere.
So what did Melville think of Pollard? Melville said "To the islanders he was a nobody—to me, the most impressive man, tho’ wholly unassuming, even humble—that I ever encountered.”
Hardly the basis for a narcissistic lunatic.
I know it's easy to think of Brody as the hero, but I think he is simply Benchley's version of Ishmael. The real story is what happens to a man after living through hell, and Ishmael/Brody are there to tell the story. This is why both characters are fairly bland with no knowledge of whaling/sharking prior to the fishing trip. This is to allow the reader to understand how men like Ahab/Quint/Pollard can be affected by life changing events that most men will never have to endure. We will never understand what happened to them, but we can observe their subsequent behavior.
I'm pretty sure that you thought that taking an ax to the radio so Brody couldn't call for help was the action of a madman, I see it as trying to tie up the loose end of being able to call for help, which is not what Pollard was able to do. The Indianapolis was in much the same situation, which Quint explains in his drunken monologue. They couldn't call for help because they had been on a secret mission to deliver the atomic bombs that were later dropped on Hiroshima and Nagasaki.
Was Quint an arrogant narcissist? No, I don't think so. He was forged by a terrible incident into a man with a singular purpose in life. His death was necessary to the character in order to show how far he would go towards that purpose.