It just seems like such a ridiculous comparison to me. As others are arguing online, Black Widow and Supergirl are two VERY different characters, and a lighter and more "rom-commy" take doesn't seem nearly as inappropriate for Kara as it does for a hardass assassin like Widow.
It's not about them being very different characters it's about the general handling of female characters which the SNL trailer parodied quite well. We're shown these strong, powerful, images of the male Avengers and when BW is introduced we get a pop song and her breaking a heel while walking to work.
It implies that you can't do a female-centered movie without reducing that female character to clichés, and to that extent reducing the entire tone and look of the show to a cliché.
Now, it'd be one thing if "aw, gee, klutzy Kara" was a "disguise" she put on like the one Superman puts on in the Donner Superman movies but the trailer suggests that this more-or-less actually Kara (why she's wearing the glasses is unclear) since she has no need for a "disguise" since she's yet to take on a superhero career.
Then we get other cliches,
The Devil Wears Prada-esque workplace dynamics, her acting goofy and unsure of herself around males. It's not-for-note a old, tired, trope that many rom-coms have used for decades and there's no need to do it.
Yes, there are klutzy, awkward, young-women out there struggling to make something of themselves in new workplaces in the city but we've seen this and had it numerous times. How many TV series have been centered around such a thing? (Felicity, Ugly Betty, to name a couple off the top of my head which seem to more-or-less fit under that heading.)
Short of, maybe say, a Spider-Man show could you imagine a male superhero show being presented in such a way? I mean, there *are* awkward, social-misfit men out there trying to carve their way in the world. So, could you see there being a show centered around Superman where as a pre-Superman Clark Kent he's stumbling around with a pop-song playing in the background, gushing, and aw-geeing with awkward smiles?
Or is it more likely we'd see him as more-or-less confident but likely just "invisible" to his co-workers and superiors. Maybe he's a klutz, or a touch awkward but not likely to the extent we see Kara shown here. (I know we don't see her literally being klutzy, breaking a heel, or anything but I think more for her stumbling for words or her awkward, toothy, smiles.)
What would have been the problem with showing Kara as being strong and confident? Coming into her new office ready to take the world by storm instead of fumbling to be noticed by her new boss? She doesn't wear thick glasses, maybe some kind of more modern and fashionable eyewear if she "must" for some reason (glasses to give her better close-up vision because her Kryptonian vision makes her way too "far sighted" and she hasn't learned to focus in her eyes yet?) She dresses how a young woman dresses in the 21st century instead of with the awkward-looking ballet flats, draping sweater and long skirt. And she's immediately taken in by her boss as standing out, an example for everyone to take notice of.
The trailer does pick-up when the SG stuff starts, but it's that first bit where it almost precisely tracks with the SNL trailer gives one a lot to be worried about and pretty much proves the point SNL was trying to make. A network/production company "getting women" by presenting them as having all of these clichés. Yeah, women like this exist. But women the exact opposite of this ALSO exist and I'd argue are likely a lot more common.
Again, I'm not writing the show off at all it looks sort-of promising and being a CBS show, I'm just glad Kara isn't working in a freaking crime-lab. (CSI: Metropolis!) but I just hope it's not as full of coming-of-age young-girl cliche-filled stories like it appears to be from the first part of the trailer. (Though, I suspect, I'm also not the target audience for the show.)
If the show can get past these cliches it started off with and show Kara as a strong, independent, woman - in any "secret identity" she may have- who's not always fumbling for words, to get noticed by her boss, flashing awkward smiles, etc. Then it could be a decent show even if it's not my cup of tea.
It just gives one a *lot* of pause when the first part of that trailer was almost note-for-note similar to the SNL parody.