I mean, she's had a secret identity for as long into her existence as Clark has dating back to Pre-Crisis, so it's not like it's out of character. And that stuff was present in the TV show and in most adaptions of Kara, which help popularize it.
I do agree she doesn't need to be into journalism but just because she has a similar situation to Clark doesn't mean she has to come off like a female equivalent to Clark because she has an entirely different background and character so she relates to it differently.
Realistically what happened to Kara is something someone would never really recover from, or at least it would be far more difficult to process than what is usually allotted to comics or what stories are allowed to explore.
I don't really jive with the idea of Kara not loving Earth, at least not without the expectation that she would grow to love it unless you want Kara to be in space all the time. But I think that's limiting her character. Even with them trying to insert Kara post-WoT she's still on Earth because of course she is
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To each their own. True Grit Kara never quite worked for me
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