On the Greyhawk Grognard blog, Joseph has a poll asking which of the Star Trek series people would prefer for an RPG setting. I went with the original series; it's the most like a sandbox. Specifically, it's the most like a sandbox with sketchy details meant to be filled in during play. I don't think tons of setting detail is important to a product, particularly for a setting that's already well-known and well-documented
But I'd go even farther and limit the core mainly to "The Cage" and the first four episodes of first season TOS, with a couple tidbits of information from other episodes. Part of the reason for this imposed limitation is to avoid the more problematic episodes: no transporter errors creating evil twins, no parallel Earths, not as many godlike beings knocking around. But it's mostly about the feel of the Star Trek setting in those early episodes versus later episodes.
Consider this: in the first few episodes, it's established than the Enterprise has a pretty far range. In a couple weeks, they can travel pretty far. But Earth colonies seem to be pretty small and scattered, and there don't seem to be many other fully-developed known worlds. Vulcan is implied, and there may be a couple other space-faring civilizations equal to Earth in development, but we don't hear much about them yet.
You get a little bit more corroboration in some later episodes: the Romulan War seems to have been more like a couples space skirmishes and attacks on each other's colonies before finally settling their differences; neither side got anywhere near the other's homeworlds, nor does there appear to be much information gained from third parties, which you'd expect if there were heavy interstellar trade.
The last TV series, Enterprise, tries for a similar feel as TOS, but fails miserably. Instead of expanding into what seems like a mostly empty frontier, discovering new things, we have humanity as a dewy-eyed newcomer into a somewhat decadent interstellar community. Almost everything's been discovered; Earth is just now finding out about stuff everyone else already knows. The message appears to be "we're younger and better" -- referring both to humanity's place in the galaxy and to the placement of the series in relation to the previous installments of the franchise.
What I'm thinking is: if you want a real exploration-oriented RPG with a sandbox feel, you need to strip back anything that resembles later Trek, with its heavier interplanetary trade and threat of large-scale war held in check by godlike beings.