Well, my want for a Rogue Trader game (cause it isn't just the character, it is also 'overarching theme of a game in which this character would work') is definitely… Not normal for the game or setting, exactly.
I was thinking of one theme that isn't done much with 40k is a game that does something like, 'choose a goal for how to affect some sort of drastic change of the setting. Do your level best to make that change. Good luck!'
I'm thinking a highly-resourceful group using the Rogue Trader system (as of the systems, that is best for people with the ability to maybe make a change), and ALL the player characters are designed to 'want to change something', would be interesting.
Take a setting that is very much designed to be stagnant (or at least very, very, very stable), and see if it is possible to actually affect positive change on it -- especially if that change was intended to brighten some of the darkness (!). Or, they could fail miserably... but trying would be fun.
I was choosing Rogue Trader as the primary (with imports as-needed from the other books, like Ascension, say), is that it inherently places you as a sort of person who might not love the Imperium exactly (but who could still plausibly love Humanity in general), who might be okay with committing some preeeettyyyy big heresies and crimes out in the Expanse past the Halo stars, because the idea for the character I wanted to play has… well, like I said, quite a lot of unique goals; I liked the idea of a character that would work best where they are all members of a Rogue Trader's ship who each want to change something big about the big, stagnant/stable/decaying Imperium, and everyone is working together to achieve the groups' mutual goals…
That said, for those of you interested in playing (and who like this theme!), if you had to make a character who had some 'big goal' regarding changing the Imperium, what sort of character would they be, and what would the goal be?
I mean, the largest change i can think about is probably when Magos Arkhan Land found the designs for his Crawler. Not the Speeder or the Raider, the Crawler. That tractor is used all over just about every agri world in the Imperium, and dramatically increased the quality of life of a lot of people. Now consider a Rogue Trader who wants to 'find' (whether they find it or, uh, 'make' it from reverse engineering archeotech and xenotech or engaging in [gasp] iterative research! Something you could only safely do in the Expanse...) the Next Big STC Template, and get in on the ground floor on manufacturing / distribution / trading / licensing of it... and make a whole TON of money, and bring a few points of light into the Imperium. That could be one of the goals regarding 'changing the Imperium', but other ones could work too.