He looks up to them in his own series history and has always made an aspiration to joining their ranks to be a part of something greater. Cap and Tony think Spidey would be one of the greats when they eventually pass on the new generation to him and other heroes. This isn't a question of whether it's a good idea, it's more like when is he gonna be there, of course Marvel had to make jump through hoops to make his induction to the team meaningful as a step of growth and progress for his whole canon life, it's one of the things Spider-Man personifies, when Spider-Man becomes ready to change into a new role, it's promoted as a equivalent to a Marvel event because Spider-Man represents coming of age and maturing.