Spidey isn't all about just cracking one-liners and telling jokes but even telling jokes in some of his most dangerous and serious moments is an integral part of the character. He's incredibly verbal. Look at the HS fight for example--it's not as if he was cracking jokes the entire time. He was talking quite a bit though i.e. trying to make Connors listen "Let's talk this out." Although a few humorous quotes were thrown in there, "Don't...make...me...have...to....hurt you! Ahhhhh!" and then of course there was him just voicing his thoughts, "Uck, that is disgusting!"
Spidey talking or even making jokes doesn't necessarily take away from the seriousness of a scene. Being verbal in any situation is a very important part of his character and one that needs to be utilized imo. Raimi hardly used it and his Spidey suffered because of it. Same with not using practical webshooters per his reasoning.