So let me get this straight here:
So because Rise openly made light of the fact that her measurements are available to the public, she's shameless? Poking fun at an incredibly sexist/demeaning practice is shameless? Is that the logic at work here? Because I think you're being incredibly harsh here. Like, to an unreasonable degree.
Once again, Rise making light of the fact she's objectified from is not shameless. It's pretty obvious that she's joking around, because she's comfortable with her self image and is obviously poking fun. (And it's worth considering the context; she brings it up because of Teddie's hospital shenanigans). Yukiko's inability to to cook doesn't preclude her from being a textbook nadeshiko when she practically embodies it.
My intention isn't to discredit Yukiko's social link, because I don't it's that shameless, but to argue that Yukiko's slink is any less of a wish fulfillment than Rise's is frankly absurd.
Again, please refrain from putting words in my mouth. I said it was one of the most genuine friendship's in the game, not the most. She uses it several times throughout the game (off the top of my head, she uses it during the news years eve sequence and a random food court meeting sequence). Upon retrospect, yeah it might not be an affectionate nickname, but regardless, trying to pigeonhole her playful nickname in the same category as Yosuke's disingenuous jabs is asinine. There's a very clear difference between the harmless nickname that Rise gives to Kanji and hurtful jabs that Yosuke constantly throws out. In Yosuke's case, nearly every single joke i've seen falls under the latter... he definitely crosses the line. Rise's "nickname" simply isn't on that level... It sends a completely different message. Kanji is obviously unnerved and bothered by Yosuke's jokes (even Chie has to specifically point that out to Yosuke) but it's patently obvious that there's no deeper meaning in Rise's jabs.
As for your second point, allow me to elaborate. She tries to set him up with Naoto during a study group meeting, and once again during the ski trip because she realizes he has a big crush on her. It's true that she's constantly crashing at his place (much to Kanji's chagrin), but I still think that's a symptom of her being a thoughtful friend. Aside from the investigation group, Kanji is pretty much friendless, and he's the type of person who seeks company/acceptance. And come on, Kanji is the second biggest tsundere in the game, so it's a given he'd be overly reticent to her company.
TL;DR She knows he's still a huge loner, so she's trying to help him break out of his shell (as evinced during the P4G shopping trip event). And then there's the band even that you yourself brought up.
It honestly feels like you're conflating general cattiness with lighthearted ribbing between teenagers.
I (grudgingly) concede, to a certain degree. That said, I found her social link to be enjoyable, in spite of the repetitiveness. (Especially her P4G exclusive Slink)
