The “Supergirl is shallow” take is a failure of reading, not a failure of the film
The complaint keeps taking the same shape: Kara doesn't seem to care enough… the horror around her doesn't land… the whole thing feels weightless. Blah blah blah. But every version of that complaint depends on the same move treating the absence of narration as the absence of meaning.
Start with why Kara is like this at all. She isn't just a sad character for mood's sake. Her parents and her entire remaining home died slowly of Kryptonite poisoning, which is the actual reason she was sent to Earth as a kid, and it's the wound this whole movie is built on top of. The film chose to show it in flashback and trusts you to carry it forward into the present, where she's drinking her way across the galaxy instead of living. That's just a character whose interior life the film refuses to caption for you.
That refusal is exactly where people get lost. Kara picks a fight with Ruthye over nothing, and it looks arbitrary if you're waiting for the film to explain it…but it's not arbitrary at all, it's guilt with no legitimate target landing on the nearest person instead. Right after, she flies off alone and screams and cries briefly in the vacuum of space, where nothing can hear her, before pulling herself back together and going back down to earth.That's literally a full emotional beat, cause and effect and recovery, without a single line of dialogue explaining jt. It's legible if you're willing to infer feeling from behavior. It reads as empty if you're waiting to be told what to feel.
The Vran family death gets the same treatment, and it's the clearest case of people mistaking restraint for laziness. They aren't victims dropped in to manufacture stakes. Remember they literally sold their own daughter into marriage, then tried to buy her back by selling out Kara and Ruthye, and Krem kills all three of them anyway. That's a complete moral arc: desperation curdling into complicity, and complicity getting punished. Calling this shallow requires either missing the betrayal or deciding it doesn't count because nobody stopped to underline it for you.
Even the "no bright colors" complaints fit the pattern. People are asking a film about grief and numbness to look and feel like Superman, and treating the mismatch as a flaw instead of the actual subject. Superman told Lex Luthor that being human means screwing up constantly and trying again anyway…that's a story about someone who never stopped trying. Supergirl is the story of someone who did stop, for a while, and the tone is doing exactly what it should while she's in that state anyway.
None of this is a hard read. It just requires accepting that a film can tell you something without spelling it out for you. The people calling that shallow are the ones who needed subtitles for the emotion.