It is also important to note that representation issues aren't limited to overtly sexualized designs - female characters are often in other ways treated poorly; existing not as characters, but as plot devices to be violently discarded to force an emotional punch or move the story forward. Some examples that jump to mind;
Talion's wife in Shadow of Mordor only exists to be immediately killed to provide Talion with a motivation. In Watch_Dogs, Aiden's niece getting killed is why any of the plot happens in the first place. Aiden's sister is only in the story to get kidnapped, and hacker ally Clara is killed off purely to force an emotional moment. All of Batman: Arkham Knight's prominent female characters must at some point be saved by Batman - Poison Ivy in her plant panties, Catwoman with her catsuit zipper always half open. Barbara Gordon is treated especially poorly in that game - one scene depicts her getting shot by Joker in a flashback (which only serves to create extra drama between the Commissioner and Batman), another shows her apparently committing suicide for no reason other than shock value, and another yet sees her used as a bargaining chip by the villain and then tossed off the rooftop anyway. Tomb Raider features that pointless rape-y scene at the start and a bunch of overly graphic, excessively violent, almost fetishistic death animations for Lara. Lady Igraine in The Order: 1886 has a cringeworthy scene where she basically tells a throwaway NPC how much of a though female character she is - which is followed by her getting her back broken in her first (and last) real on-screen fight, and her 'arc' ends in a cliffhanger with her being irrationally angry at the male main character due to a misunderstanding. Quiet in Metal Gear Solid V 'breathes through her skin' because she gets burned alive and falls out of a window in the intro of the game, after which she is involuntarily subjected to cruel treatment. When she is tortured later in the game, the camera still lingers on her chest.
You wrote a great piece and I wish I had time to reply to all of it, but I'll pick this one section to discuss.
A loved one dying to provide motivation, plot advancement, or an emotional moment isn't limited to female characters. It's really just a writing trope. I think it's perhaps easier to find examples for you because of there being so many straight male main characters, thus they have female loved ones for bad things to happen to to advance their plot. There are plenty of examples of "men being treated poorly to move the story forward".
- Ezio's father and brothers being executed in front of him in Assassin's Creed II
- Joel
being injured at the end of Spring so that Ellie takes over for the Winter section and DLC
being killed at the start of Horizon Zero dawn to spur Aloy towards revenge and finding the Eclipse cult
Also re: "All of Batman: Arkham Knight's prominent female characters must at some point be saved by Batman",
Poison Ivy saves Gotham and Batman from the Scarecrow's Cloudburst/Fear Gas. She sacrifices herself to do so, so I suppose it's a wash by your standards. (though she remains as an orchid, so it's hard not to see her returning to life via some comic book bullshit, but that's neither here nor there.)
I also think singling out Tomb Raider for its now infamous death animations is kind of silly. Video game heroes in general suffer horrific deaths.
Should Lara Croft (and female protagonists in general) have less violent death scenes than their male counterparts?