Hi! Okay so, I’m not sure of what exactly you’re asking, since you’re wondering about relevance but at the same time all your examples about Touka are relevant to explain her character, but anyway I’ll try to expand. 

First of all, maybe it’s a question of word choice, but as an “individual” your only role is to exist and live your life to me, so I’ll personally speak about Touka’s characterization instead: 

You were wondering about why Touka fights even though all she wants is a peaceful life? Well, what good is your “peaceful life” if there is no one by your side?

So the reason Touka fights is not because she believes in coexistence and thinks that her peaceful life will come along with it. On the contrary, she sees her own species in a more negative light than humans, going as far as to not even see herself as someone who would ever be “beautiful” because “she’s a ghoul”. 

No, the reason Touka fights is because she can’t just live while losing things and people. Not anymore. Initially, this philosophy was one she probably tried to live by between TG and :Re after Yomo told her to run away from the 20th ward:

But after Kaneki/Haise came back, this philosophy began to shatter. She went to help Tsukiyama’s escape during the Roze arc, she went with Ayato to save Hina in Cochlea and now…

She’s most likely going to save her husband. 

Again, this has nothing to do with coexistence. She doesn’t want to save “the one eyed king, so that he’ll stop rampaging through Tokyo and kill humans”, rather she wants to save her husband because she loves him and because

…she’s building a family with him. 

And I spoke about this before, even if it’s not really the subject here, but Kaneki is exactly the same.
The OEK role was initially given to him by Eto and Arima, and the only reason he accepted was because at the time he had nothing else to focus on in order to keep on living. It’s different now, because of his love for Touka and yearning for a future with her, which is the main reason he ended up going berserk recently:

So you could call that “selfishness” if you want, but looking at the whole story, Touka and Kaneki are characters who could be summed up (in my opinion) by “I was selfless for a long time and I really tried to help everyone else, but now fuck it I come first”. 

That’s why deep down neither actually give a single care about the current conflict. Or well, they do, because ending it means their friends not dying anymore and that Kaneki will stop being a leading figure, but ultimately it’s about themselves, not about making the world a better place (they might eventually come to that though, for their child’s sake, but it’s not the case right now). 

In other words, Ishida called them a set, and a set they definitely are. 🙂 

Back to Touka, one of her biggest issues to solve in my opinion before she get to live a peaceful life would be finally accepting that ghouls aren’t inferior to humans, which is something she doesn’t see right now but which might change…

• through finding out what happened to Arata, since his fate is one more proof that the CCG, a human organization, did terrible things too

• through meeting again with Yoriko, who now knows about Touka being a ghoul and who still sees her as a precious friend anyway

• through giving birth to her baby, which would help her with seeing herself in a different light.

Finally, if we were to speak more generally of Touka’s relevance in the story (since it seemed to be your original question), then I think the one mistake not to make on the subject (and that unfortunately more than a few readers do) would be to define her character based on the romance between her and Kaneki. 

In fact, both Touka and Kaneki, even if they were described to be a set, are not solely defined by the mutual love they share. They exist as two different individuals and falling in love with each other is but one part of their respective characterization. 

Anyway, so if I were to give an image to explain Touka’s relevance from my point of view, I’d describe her as everyone’s pillar of strength.
Example: to be quite honest, even as a huge fan of hers, I was almost convinced that Tsukiyama would be the one leading ghouls during that common front with the CCG, but guess what…

I was wrong. And it’s extremely interesting because, as I was saying above, Touka isn’t and doesn’t want to be a leader.

She isn’t even vouching for this common front because it’s important for the ghouls’ rebellion and for coexistence, nope, and yet she’s the current leader figure after Kaneki went Dragon, which speaks a lot about how many characters look up to and respect her because of what she represents and did for them.

Even Yomo, who used to be like a mentor figure and who was the one who told her that “they could only live while losing things”, apparently left that philosophy aside too, probably because seeing Touka and Kaneki falling in love and wanting to build a future for themselves changed his mind.

So Touka’s relevance as a character has always been like a huge light shoved in the readers’ face throughout the whole story in my opinion, which is why I’m baffled whenever I read people saying “she isn’t doing anything” or “she’s just Kaneki’s love interest”. 

In fact, that’s the contrast with Hide’s own relevance as a character to the story (since people who shit on Touka generally love his character). He’s as relevant as she is, but it’s for different reasons and it’s also not expressed similarly in the story because of his strong shady game, which is why both their dynamic with Kaneki are interesting. 

In other words, Touka and Hide are both relevant, but for Touka it’s written in an almost blinding way while Hide shines too, but it’s as if it comes from behind the stage TG’s story takes place on.  

There, it was long, sorry for rambling. Anyway, I don’t know if this helps? You seemed to be wondering about Touka’s relevance as a character, so I hope I could at least answer this, if that’s what you meant.

Have a nice day Anon. 🙂