In the spirit of the Human Urge to Defend Opinions on the Internet, I do genuinely like Princess Thira, but I also have a lot of thoughts about her that demands some nuance
-Girl pretty, magic cool, relatable for hyperspecific personal reasons that I won't get into because they fall firmly into "my business" and therefore should not be brought into a discussion about a character's objective quality, damsel trope make brain go brrrr, and I'm really taken with the potential behind her.
-No, not really. I don't think the writers can fix it within the structure of the story they have built either, but I DO hope!
-I don't really think so. If anything, she's a MacGuffin, but that feels like splitting hairs so I don't really burn too many calories over it. More on the Mary Sue thing later
Do I hope she ends up in a canon romantic relationship with the Slayer?
-No. Speaking from the canon (bible definition here) lore, it's not a good idea. She isn't a structurally sound character, and it would desaturate the meaning behind the Slayer's character and utterly obliterate what little impact she has anyway. She doesn't have a clear personal motive, she doesn't have a cohesive development arc, she doesn't have any meat to her writing besides Fridge Mom and Cool Powers.
Am I going to keep shipping them?
-Yes! At this point in my creative style I'm not really the type to create a self insert (could change over the years, who knows). I love seeing everyone else's self inserts and I've loved what everyone has done here, it's just not my style right now.
I like the IDEA of what a relationship between two characters like them COULD be. I liked it so much that I wrote it myself! I don't need the canon to tell my story for me to feel validated, and even if they do end up a thing, I'll never be entirely satisfied because I like my interpretation a LOT more than what the actual source material provides. The Doctrine fic IS an alternate timeline where Eternal pretty much doesn't happen. It's my own little dollhouse with a Barbie and a G.I. Joe, and I've learned a lot as a writer and had a lot of fun with it, so it suits me more than anything I could consume anyway.
I think it is worth considering the lack of women in DOOM. They're either villains or Dr. Peterson, no complaints about any of them, but I appreciate the attempt to put a heroic woman into a setting that is overwhelmingly masculine. Women in fiction are (unfortunately) difficult to write in a way that people like anyway, and you WILL catch flak for any kind of attempt, particularly when the audience is largely chud-dudebro or incel-gamer type guys. I am a bit of an apologist about this, but I hope to make up for it by aiming to write my own women as cohesively as possible--and I only get better with practice. TO BE CLEAR, I also don't think it's an excuse for why Thira objectively isn't good. We ought to have high standards for the media we consume, as creators. I can, however, see why they failed, and I hope to better understand HOW so that I can be better in my own work. I think it's a call to action for those of us who write and draw. Anyway, that's why I don't really care for the term "Mary Sue". It feels like a buzzword for "Woman I Don't Like for Reason X/Y/Z" to me, rather than something constructive aimed at solving a really prevalent problem in media. It's healthy to understand failure and try again later, that's what critique is actually intended to be.
EDIT: I really do truly like her! I like her for the same reason I like cookie dough oat milk ice cream: it satisfies a taste, and that’s all liking something has to be. I’m not about to get in a fight over ice cream, so I’m not going to double down and pretend that she’s this groundbreaking character that changed my life and psyche, I just like her! I like all of the characters (ranging from “neato!” To “I’ll jump off the porch and kick your ass”). I like Doom! It’s fun and its cool!
TL;DR - She's cool and pretty and more likely to kiss the Slayer than me, so I like her. There very literally isn't enough there to say anything else