While Litchi is a playable character, and has her special theme music versus Arakune, she is still considered a supporting character instead of a main character. The whole deal with Arakune, to put it bluntly, is considered nothing more than a filler subplot to the whole story. What I mean is, that while it is impressive and adds to their character development, it hardly connects to the overall story or our main protagonists. It's similar with Millia's quest in Guilty Gear, and one might argue that the whole thing was simply to mirror Millia's rivalry with Zato-1/Eddie. In the "True Ending" of both Calamity Trigger and Continuum Shift, the ending that would destroy the repeated cycling of time, with only Ragna, Jin, Noel, Hazama, Rachel, Kokonoe, Hakumen, Jubei, Nu-13, and a bit of Tager played a part in the conclusion. Why didn't the rest of the characters showed up? Because their stories weren't significant enough to add on to the in-depth storyline.
But I digress. While Litchi isn't considered important enough to be one of the stars of the game, I think it's inaccurate to also say she is a useless character. Her role, though small, still makes an impression on our main cast.
In the first game, Litchi makes contact with our main protagonist, Ragna the Bloodedge, in his Story Mode and hers. On his journey to annihilate the NOL of Kagutsuchi, he is threatened by Arakune, who desired for his Azure Grimoire. Before he punished the beast mercilessly, Litchi interrupted and begged him to stop. After a short discussion, Ragna withdrawed and left Litchi to deal with Arakune.
Litchi and Ragna are almost in a juxtaposition. Both had obtained power that didn't belong to them - Ragna with the Azure Grimoire, and Litchi with her Boundary power - and both used them to solve their personal agendas. And yet their paths were entirely different. To the Grim Reaper, Litchi had a very noble objective: she wanted to find a cure for her friend, using the least amount of bloodshed possible. Despite the damage Arakune caused, she was willing to take full responsibility for his actions, and would risk her life just to save him. Ragna, in contrast, would kill anybody that opposed him, unless they were good friends (or ladies apparently). He also could not forgive his brother Jin for betraying him so much that he was half-heartedly willing to kill him.
Litchi's actions may seem to provoke Ragna to alter his methods. Note that Ragna's Story Mode splits off after this scene depending if you tempted to kill Arakune anyway. If you chose to spare him, you end up with Ragna's "Grim Reaper" ending, which is the closest to the canon ending for Ragna. However, if you didn't have any concern, you would end up in a random scenario with Taokaka, which is more for humor than anything serious. In addition, when he faced Jin, his own rival (as Arakune is to Litchi), he defeats him but lets him live. Jin responded that he's "too soft", which can also be a trait Litchi possesses as well. It was almost as if her light moved him.
Aside from all that, Litchi broke the status quo by being the only character who isn't interested in a piece of Ragna. Her search for him is immediately cut half-way through Litchi's Story Mode, and even then, it is possible to not fight him at all and just talk. When she is questioned by Noel, she saves Ragna, a man she didn't knew well, from being captured by NOL. It may seem insignificant to some, but the premise itself supports the relationship between she and Ragna. He would be comforted by the fact that not everyone was out to get him, and may even soften up more to people.
The sequel especially opens up more room for Litchi's involvement with the plot, what with her joining NOL and all.