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That's EXACTLY why she was created. Marvel got word that Hanna-Barbera was planning a "Spider-Woman" cartoon, and rushed out their own character with that name. Fortunately, they got Archie Goodwin to write the first one, so at least it was a clever concept, well executed. UNfortunately, a later writer decided (much like Shooter with the wall crawling ability) that having her be a super-evolved spider was "icky" and so the one thing that made her interesting was undone.

She-Hulk was created for similar reasons.

Spider-Woman was apparently created to be as far from Marvel's Spider-Man property as possible while still remaining true to the name. The costume carries over the shape of the eyes and it could be said that her "glider wings" are reminiscent of the original Ditko under-arm webbing Spidey used to sport, but really, as far as they could, the creators of Spider-Woman went in their own direction.

Creating webs is just one thing spiders do. Gliding is another (albeit somewhat more uncommon.) Creeping people out on instinct is yet another. (This was something I was sad to see the character lose. Originally, strangers just found her off-putting and unlikeable since she evinced in others the same feeling spiders do when you first see them...) 

As a range weapon, Spider-Woman has her "venom blast" instead of web-shooters. Creatively, she was all about differentiation. West Coast vs. East. Red vs. Blue. Even inherently unrelatable vs. the most relatable character in comics. Really, the more dis-similar she is to Spidey, the more I like her.

Following the logic through farther, why didn't HYDRA equip every single member of it's army with web-shooters? And shields as close to indestructible as they could get? And stolen Stark-tech armor? With flying Falcon wings? And crescent throwing knives? And a retractable billy club? And trick arrows?

Once the tech is out there, everyone's trying to copy it, right? Why isn't every single bad guy on the street a walking Super-Adaptoid?

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Somewhere, Mark Gruenwald's head just exploded.

You know, I don't believe I've actually read a Spider-Man comic in about 30 years. Does he still use the Spider-Tracers? I used to love those things

I did too. In fact, I think this touches on why many of us feel so strongly about the web shooters vs. organic. The web shooters are COOL! The spider-tracers are COOL! It was very fun as a kid to imagine the web shooter mechanism, pretend you're wearing it, doing the double finger tap on the palm to release the web fluid. Organic web shooters, among all the other criticisms here, are just...boring.

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Another rather foolish retcon! Too many people started asking "how can he make a fist without spraying webbing, if the firing button is in his palm?"

There MUST have been a better answer than "He has to tap twice". In the heat and ferocious speed of battle, even the fraction of a second between taps could have meant the difference between life and death!

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If we are looking at the spider bite to so comprehensively rearrange Parker's DNA as to create webshooters in his wrists, along with the tubes that would feed them, and the organ(s) that would generate and store the web fluid, all completely contrary to how a spider's webspinners are configured -- well, given all that, growing a few extra limbs would be a snap!!

JT, here you go:

(Every time I draw Michael Golden's spaghetti webbing, I remember that a half inch thickness could "hold the might muscled Thing a prisoner for life!")