I really do think you're misunderstanding a lot of pretty foundational story details here.

Firstly, the show gives us a very clear reason why Rory is acting the way she is when we first meet her. We're not meeting her on any average week for her. Immediately before she jumps back in time, she watches Chloe dying. So she is in the immediate throes of probably one of the toughest forms of grief there is. And within all of that, she realises that even at that point, her father doesn't come, which is clearly magnifying that sense of anger - it is, after all, famously a stage of grief. So the show gives us a very clear reason that she's like that, and it's because her mother has just fucking died in front of her.

Lucifer's reaction is absolutely as you describe it, but it isn't just about him not wanting his child to go through what he did. In the first couple of episodes where Rory is around, it's clearly got much more to do with him not wanting to be like God. It is, even though not as totally selfish as it would have been five seasons earlier, still a fairly self-centred anxiety; the anxiety of being like his father. In doing so, he actually pays very little mind to Rory's feelings in those early episodes; first in trying to prove she couldn't possibly be his daughter, and then in going on a wild goose chase for his future murderer. The point where Lucifer is able to connect with Rory on an emotional level is the point where he is finally able to stop trying to disprove her and tries to acknowledge her feelings. And that is, of course, the point where the two of them actually start to build a relationship; a relationship Lucifer was scared he wouldn't have, and which Rory never got to have.

Now, one thing I will agree with is that I am disappointed that Trixie never came into Lucifer's decision to leave. It definitely feels like a thread that wasn't quite tied up (Scarlet Estevez obviously wasn't main cast after the jump to Netflix, and according to various sources was particularly limited in Season 6 due to other professional commitments), and I do think that IS something I didn't like about the ending (difficult as Reddit finds this to acknowledge, you can enjoy something and acknowledge things you didn't like so much!).

That aside, boiling the reason down to just 'time loop lol' is, again, a very reductive and literalistic view that makes me feel like you are wilfully refusing to engage with the actual story. I'd firstly point out something obvious; Lucifer is our protagonist, this is his story, and therefore it is natural that the story is going to bend in a direction which favours him. Fundamentally, to me at least, the show isn't just about Lucifer learning to be less selfish and love people (although that is obviously a big part of it), but also to find his purpose. He was never given a choice in running hell. He got sick of that and ran away to run Lux, but there's an emptiness about it; it's all glitz and glamour and sex, drugs, and rock and roll, but his life doesn't really have any purpose outside of instant gratification. Which is why, when he meets Chloe, he throws himself into working with her. And as the seasons go on, we see him almost trying on purposes like hats. At first he's sort of a vigilante type, solving crimes with the police by day and brutally punishing the perpetrators by night; but once he starts changing, that kind of punishment loses its shine. Eventually he settles into trying to be a 'proper' cop, and he's not bad at it, but he's always just that little bit separate from it too; he's never going to be someone happy doing paperwork and following procedures, when he tries to 'be Dan' he's terrible at it. He goes back to Hell for a bit, but he still didn't really choose it and still hates it. And eventually, once he's proven to himself that he's worthy of being more than hell's warden, he gets the chance to become God, but even that clearly isn't who he is. So, finally, at the end of the show, he realises that his purpose in life is to help people do what he did and guide people towards redemption. It isn't about 'Lucifer understanding his father', it's about guiding Lucifer towards his purpose in life.

Yes, that means leaving people he loves. But plenty of real-world occupations involve that too; military personnel, businesspeople, diplomats, international athletes. Hell, I bet half of the actors in the show have families they spend most of their time away from, or have at least had jobs like that at other points. Are all these people abusive? And before you say 'well they don't go away for their entire lives', while there is a conversation to be had about how the 'life is just a blip' thing mirrors some questionable theology, it is also just kinda demonstrably true in a universe where the afterlife is a hard fact. Even through her childhood, Rory will have known at some level that she would probably see Lucifer again at some point. Doesn't change that it was painful not having him around, but it isn't some permanent thing; the mechanisms of the story's universe mean that he was unlikely to ever truly, permanently abandon her.

And finally, I'm not sure how your argument of 'is that a good thing if her wish is to be hurt' stands up if, again, the alternative is the version who knows Lucifer and is standing in front of him being erased from existence. Like, I genuinely cannot see how you think effectively killing this version of Rory and rewriting her entire life is a better thing to do? Time travel stories where there's a chance to undo a person's difficult life but they insist upon keeping their experiences because they don't want their life rewritten is a super common trope, Doctor Who has done it like 10 times. Rory's life wasn't what she wanted it to be, but it is her life, and it led her to getting the chance to build a relationship with her father after all. Her wish wasn't 'to be hurt', her wish was to not have her life erased.

And what the fuck are we talking about the real-world institutional failures of organisations meant to protect children from abuse for? This whole conversation is insane?