I mean, I think it does. Spider-man is a timeless iconic story that is based on the kid in all of us but the man we will become. I think Marvel should some how reset Spider-Man back to being 16 and somehow start incorperating the modern age feel of what Spider-man stands for, like Blue Beetle for starters. Replacing Peter for someone else would not be wise since thiers only one identity that people know of Spider-Man, Peter Parker. And somehow the 616 verse will have to change to, maybe not entirely but to the point where Peter is young but not so amateruish when being in the hero scene and is more a myth than a fellow hero in thier world.
Personally I'd would want to keep Amazing Spiderman running so I can see Spidey being one of the top brass of Avengers and not a fanboy status guy who tells jokes, appriated enough to be a name just like Cap and Tony but not entirely whorshipped as a god, just to show some relevance in over 50 years of printing Spidey. Maybe as far as his underdog status, I'd at least make him stary from epic adventures like the other heroes and stick the NY as the top street level hero and maybe team up with the team only to be involved with his own rouges gallery in a common world wide threat or event that requires his knowledge and skills.
But I feel if they want to add a new hip feel, they should reeboot the entire series and start over. Like everyone up till this point including Harry and his father, May, MJ, and his villains would be retconed into a staring phase and become more or less like Peter is but helping him build up his legacy.