To be fair, how much did web-shooters add to being in the films that had them beyond just being comic accurate? They typically don't add any drama or have much to do beyond being an accessory. After having them for so long, especially in film, if he forgets to load them, it makes your hero look even less heroic.
As a matter of fact, the only film that used him loosing his ability to shoot webs effectively was Raimi's film. That was a whole thematic subplot of the second film as Peter was loosing confidence in himself (something that's more character accurate than anything later Spider-Man films have done) and it's actually better because of it.
Setting aside the fact that it helps establish Peter’s intellect (and the buried creativity—and ego—that the spider-bite unleashed), it also avoids that creepy/body horror factor, and is a wee bit more plausible than the organic webs (how does he generate them? Why do they come out of his arms? Does he have to eat all the time? Shouldn’t his forearms look like Popeye’s? Why do the webs project out of his arms at high velocity? What happens to him when he runs out of webbing?).
The mechanical web-shooters, being a fantasy technology, help sidestep some of those questions, and also add in story potential involving their being damaged/Spider-Man running out of cartridges, and their being adjustable for different situations (a fine spray, a thick blob of glue, a strong line or net, etc.).
The whole psychosomatic bit in the second film is just a riff on Spider-Man seemingly losing his powers in the first Lee/Ditko annual, and the organic webs were not at all necessary to that plot point, except maybe as a jokey erectile disfunction riff. Having him generally seem to be losing his other powers (as in the annual) would have worked just as well, had the mechanical web-shooters actually been in the films.
But, at the end of the day, Raimi’s reasoning was “I couldn’t build these things when I was a teenager, so it’s not realistic”, which is rewriting the character. And that’s really the bottom line with so many of these adaptations—rewriting and rethinking the source material. “How much can we throw away?” Instead of “How much can we keep?”.
If I squint, the Raimi films are reasonably on-model, but I still have a laundry list of problems with them. And the subsequent films have gone more and more off the rails. I haven’t even bothered with the two most recent films, despite Spider-Man being my all-time favorite comic character. It’s become abundantly clear that the tail now wags the dog, and the movies can and will do anything they want, with the notion of respecting the source material a distant afterthought. Familiar names stamped onto unrecognizable characters (be it due to legal issues or poor writing) and presented as mass-market “content” for the benefit of a soulless megacorporation. No, thanks. I much prefer the punk-rock artistry of the classic Marvel Bullpen.
I’ll stick to my old comics, thanks.