I'm not disagreeing with you, I just don't see why those things needed to bleed into the comics.
Because the goal of adapting comics into other media is to attract a new and much larger audience to the property. Some of those, hopefully, will start reading the comics as a result, which is a good thing, because it increases the comics audience, perhaps by a considerable amount. And you want them to find a version of the characters and the world that they recognize. If the TV versions of Bobbi Morse and Lance Hunter get people interested in checking out a Mockingbird comic for the first time, but they see a version of Hunter who's nothing like the guy they like on TV, then they're unlikely to stick around and keep paying for new issues of the comic.
It has always been thus. Superman comics sold well, but it was the radio series that really made the character a national icon. The radio series was enormously influential on everything that followed -- the source not only of Perry, Jimmy, kryptonite, and Inspector Henderson, but of the famous opening narration later used in cartoons and TV, of Superman's famous catchphrases like "This is a job for Superman" and "Up, up, and away," and so on. After all, even in those days, comic books cost money, but radio was free. The radio show reached far more people -- and it came out five days a week rather than once a month. So it had a bigger impact than the comics, and so it influenced the comics.
And today, comics sell in far smaller numbers than they did back then, because they've become more of a specialty collectors' market. The number of people who know characters like the X-Men and Spider-Man from the comics is a minuscule fraction of the number of people who know them from movies and TV. So of course it's the version that reaches the larger audience that's going to have the most influence. It's going to generate new stories and new ideas, and there's no reason why the different branches of the franchise shouldn't cross-pollinate each other with ideas. That's part of what keeps a fictional universe vibrant and growing.
Organic web shooters are not in the comic right now. They were, however, in it briefly right around the time the first Raimi film came out. I don't know how long they lasted, but they're gone now.
They were barely acknowledged after they were introduced. There was a really bad storyline where some insect-queen villain caused Peter to "die" and be reborn out of a cocoon with new powers including organic webshooters and the ability to talk to insects (even though spiders are arachnids, not insects). The latter ability was acknowledged in maybe one subsequent issue before being forgotten. The organic webshooters were mentioned maybe twice after that storyline, but mostly ignored, with the source of Spidey's webbing not specified. And only a year or so after that cocoon-transformation storyline came
another storyline where Peter apparently died and was reborn from a cocoon with new powers, without a single reference to the previous one. This time, his new powers included venomous spikes that extended from his wrists (like spiders have, right...?

). That transformation was apparently wiped out a couple of years later by the same deal with the devil that erased Spidey's marriage. (And when I say a couple of years, I mean real-world time. In terms of in-story chronology, these things all happened within weeks of each other, a couple of months tops. A new status quo barely got a chance to be established before it was upended by the next massive miniseries/crossover event.)