Quick disclaimer, not had the time to get to New Raider, though was very fond of the originals.
What it sounds like the issue with Sam is character-craft. And hardly one that's isolated to her. It's all in the emotional distances. Having read some of the other comments Sam has a long history with Lara, they went to college together and all the social and personal interactions that entails; friendship, trust, confidence etc. through shared experience. She's also poor with physicality and confrontation and evidently idolizes Lara for her more assertive adventuresome traits. (Just what I've gotten from the thread.) Great, cool, nice exposition. Intellectually, got it, friend, bestie, my main girl, whatever.
And here in lies the problem. Intimate relationships of any kind, while have intellectual components, are largely emotional and built on shared experience. No amount exposition on the planet can make up for even thirty seconds of experience. We need to be close to her, to feel for her, to motivate us by friendship. This is as true in real life interactions as it is in games.
Scenario: You've read a dossier on person X, say Jane. Shares interests, hobbies, beliefs with you, its very thorough and detailed. Someone you could befriend easily. You meet her in the street, begin to talk. A few minutes in she says she needs to go to the bathroom, then catastrophe Y happens and you witness her being taken off, captured, enslaved etc. You know here as a person, you know you *could* become friends, but because there is such a lack of shared anything you haven't invested any emotional capital. Sure, whatever foul fate awaits Jane is terrible, but the odds that you'll be motivated enough to risk your hide to save her are slim to none. You just don't care enough. She's effectively a stranger.
What makes this instance worse is that the only experience we as the player has of Sam is (quoting the thread) a sniveling whining coward who lacks any sort of agency, making her an object. Which I'm not against as a character at all. Most people just aren't cut out for trauma or violence and would respond similarly. What seems to be lacking is the context of this trauma that's broken Sam's spirit making her a mewling malleable lamb and the context of my Lara gives two farts about her.
Experience, context.