So I think there's the kernel of an entertaining idea here, regarding how idioms translate, but I have such an immediate, visceral reaction to how unfunny Pete Holmes is that I'm not really feeling charitable here. I think as soon as the woman whose head was underpants showed up, we crossed the line past anything that could be salvaged.
I'm hoping Very Short Treks started with their weakest showing. Who okayed this? I'm imagining someone who when asked what their favorite part of Star Trek is, responds, "the lightsabers and the Wookies." How else would the not at all representative of Star Trek whinge, "omg, I can't say anything without offending someone!," get put on repeat for nearly the entirety of the short. Except by someone who is clueless about Star Trek. And then ending with the Captain getting his imaginary girlfriend wish fulfilled. What the hell did I just write. What the hell did I just watch.
I'm taking it at face value that old earth figures of speech and idioms would be problematic on a TAS bridge with the nomaly going on, they addressed that by the cat person responding that "there is more than one way to disembowel a human", we wouldn't like people casually throwing that around. It's also tongue in cheek as illustrated by the knickerstonians and the ship blowing up. It's meant to be silly.
The tapestry of star trek (and science fiction) has always included silly and over the top alongside the serious, thought provoking and intelligent.
Cornering the star trek parody and comedy market with their own product is genius btw. Like how Elvis's manager sold "I hate Elvis" shirts.
One could argue that "Skin a Cat" makes a more profound point amidst the silliness. Which is that (as Azetbur has pointed out) "the Federation is nothing more than a homo sapiens only club".
Obviously there are real world reasons why human (and primarily American) cultural references abound in Star Trek, but it's always irked me that, for instance, there would be an entire class of Starfleet vessels named after cities in one United States state - ie, the California class. Why not have all the ships in this class named after towns in, say, the ShiKahr district of Vulcan instead? I think that would do a better job of world building, representing the Federation as a body that's more than just a bunch of humans with a handful of token aliens. Or, better yet, have all the ships ships named after smaller cities in a range of UFP member planets?