This is really a minor point, but it seems you missed a key element of the story in KotOR2. The Exile was the last known Jedi because she left for parts unknown before the slaughter of the Jedi by the Sith. No one knew that some of the Jedi had survived and were actually in hiding all over the galaxy until the Exile stumbled onto that info in the course of escaping the Sith. Hence, the Exile was generally known as "the last Jedi" but wasn't actually the last Jedi.
You never answered the question: what would you have had them do in the game if not have a series of goal oriented quests to drive the plot forward? What single-player RPG doesn't follow that formula in some way? Heck, not just RPGs, pretty much every game genre that has an actual story to follow uses that in some way.

Yup, its that or some lame empty open world bullshit where you wander around and get into fights for no reason. Might as well play an MMO

(Chuckle) Poor Raphael Sbarge.

It's pretty much all been covered, but:
It has come to my attention that Obsidian Studios is run by half-imbecilic chimpanzees.
Just a thought.

Actually IIRC you could get Zaalbar to kill Mission because of the oath he swore to you. Which is awful, and awesome, and so very worth it.

I did not miss it, I just said the whole thing is stupid.
— You are the last Jedi left!
— Oh.
— But, behold, there are four more last Jedi hiding on four different planets, and it is your quest to find them!
— Hooray!
Sure, there is always some main overarching goal that you kinda have no choice but to accept, else there is no adventure, a bit like if you refused to look for the waterchip and instead opened a pastry store in the middle of the wastelands. What you can do is debate of the quality of that goal, and it can be tricky to find a good reason to get people to start adventuring and maintain it during the course of the game, but in the case of KotOR2 it isn't much of a quality motivator. It is even copy-pasta from the previous game, which already copy-pasted it from the NWN OC, which did it multiple times in the course of its adventure. There isn't much to care about these four dudes, and you can kill them or let them live without any great consequences, which shows just how important your mission is.
Would have been if the two characters had been more fleshed out. Since they are paper-thin, I couldn't care less about what happened to them. Compare that to selling Dak'kon into slavery and his reaction of anguish, or throwing Morte back into the Pillar of Skulls. These two were also a tad more fleshed-out during their game than the walking carpet and his blue tentacled little sister.