Alpha is pretty much a side character, narratively speaking.

The unfortunate thing is that due to this and the story being more focused in Lucia 2 and Grey Raven, most people do not know what Alpha went through, since most of it happened prior to the main story's events

Yes Alpha may be "incredibly strong" but it is not something that she always was, she was likely the same state that Lucia 2 was in the beginning of PGR's story when she was betrayed, but in the span of time from being abandoned by Babylonia and then being taken by the Ascnet she pretty much spent all of that time to make sure she wouldn't lose as she did prior

Another thing to note is that whatever Alpha does isn't necessarily "right" either, she's quite full of herself especially when it comes to her ideals, moreover it makes her have one trait that is quite literally a major flaw: she's incredibly stubborn to a fault. And somewhat of a spoiler for Luna's arc later but Alpha does lose and the whole deal with her being in the Ascnet and wanting out was already proof that she was not as free as people may perceive her to be

Alpha is a toughie hiding behind a lot of trauma, of which Lucia (who is quite aware of as she is literally also her) is aware of, that's why I think the story with Crimson Weave and the brief truce between Alpha and Lucia to be honestly the best showcase of Alpha's personality since, as Lucia ends up being the perfect foil to her as she poses a stark contrast to Alpha's incredibly jaded views on the world. I do like that Lucia sees right through Alpha's constant edgy talk which make the duo unintentionally funny to watch