What do people like about the Inquest? I never really...got it?
I think it really depends on who you ask.
For me, the Inquest is fascinating because they're effectively a terrorist organization legitimized by the Arcane Council, but they didn't start that way. Word of God has indicated that they (may have) originated after the exodus from Quora Sum and the other lost underground cities, largely as a desire to protect the asuran people, as well as their culture and knowledge, from being lost at such a devastating scale as they experienced in that time.
And at some point, they just... lost their way.
The Inquest preys on people in the same way a lot of cults might. You'll see those (Plunka from the Transatmospheric Converter story step "Salt in the Wound" is a great example) that fell behind in asuran society promised the moon by those like Kudu, after which they're taken advantage of and tossed aside as soon as they overstep their usefulness.
And this in particular is a great way to dig into characters and their motivations! I have a few ex-Inquest characters (such as Vezz and Rhenn) who come at it from very different angles. They weren't bad people, but circumstances led them to where they were and how they departed in the end.
I also have some really dastardly evil characters who are strictly Inquest because they LIKE having no boundaries and the ability to use and abuse subordinates, other people, and other races (like Miyya, head of the Inquest Ethics Committee, or Prikk, my boy Rhenn's father/creator). These guys are just strictly nasty, mean people who revel in having no guardrails for ethical research.
And compared to the other "bad guy" orgs within the other playable races, they're distinctly unique BECAUSE there's actively a member of the Inquest on the Arcane Council and canon confirmation that the council lets the Inquest handle projects they don't want to bother with. They're basically considered a legitimate branch of asuran government to the point that they have a lab and recruitment area IN Rata Sum proper, even when the majority of asuran culture loathes them (a huge chunk of events and renown hearts in Metrica are about messing with the Inquest's operations!).
And yeah, folks like the Svanir have operations in their home city, but they're also derided and treated poorly by the people there. You're even warned before you enter those caves.
But bandits, NMC, Flame Legion? They're not legitimate in the eyes of their cultures as a whole.
In the end, it's largely what each person wants to explore. The nature of escaping a bad situation and forgiving yourself for your mistakes? Just being an absolute garbage rat who likes putting shock collars on people for fun? It's all an open book!
And when you're dealing with a group that can smugly respond "Well my boss works with Councilor Yahk so why don't you take it up with him" it really just leaves a lot of room for playing around.