Wouldn't work. There are about a dozen different reasons I can think of why too. I'll just go through some of the major ones I can make public.
1) We're not releasing concept art. Last time we tried that on BtRL 3 or 4 different BSG mods nicked it and used it without permission, some of them actually releasing our stuff before we could. I dread to think what would have happened if we'd actually had models or textures publicly available.
2) In addition to having to publish the story, FREDding requires all assets to be released. Given 1, that's out. But on top of that releasing everything we had would basically result in the team spending more time fixing the problems of people who want to play the game rather than work on it. It would be a complete support nightmare with people who have never used FS2_Open trying to play an alpha game using alpha builds. Never going to happen.
3) Look at the FRED Academy as an example of what happens if you try to get casual FREDders to work on a campaign. In the case of the Academy it doesn't matter since the main goal (at least as far as I was concerned) was to teach people to FRED. Any campaigns that were released would be a bonus. With Diaspora, campaigns would not be a bonus and the team would spend more time duplicating work already done, waiting for some casual worker who may or may not have decided not to work on the project any more or chasing after people to get them to give us what they've done so far. Again, it would be a nightmare and would actually result in slower development.
4) With an open project you're going to get an awfully large number of people applying who don't have what it takes to make stuff of the quality the team have so far. But if you're not vetting them in any way the only choice is to ditch the model they just spent 4-5 weeks working on, dump it in the bin and give it to someone else. It's just a huge drain on the communities up and coming talent.
Most of the casual workers a more open development style would get us are currently working on mods which do not need to be of such high quality. If they're fun to play we'll forgive the fact that the models look a bit ****. Yes we could help those people learn but then we'd spend more time teaching then we do modding and the quality of the mod would go down since all the work would end up being done by the amateurs while the professionals spent all their time telling them how to do things they could do much better anyway.
Diaspora, like WCS, SoL and FotG are flagship campaigns that will draw people in from the outside world. They need to look as professional as big name mods like Black Mesa source or Garry's Mod in order to do that. And that goes against the kind of open development plan you're on about.
5) If someone has the skill to actually make us something of the quality we are looking for why not just apply to join the team? We're a friendly bunch (mostly) and we are happy to take people with talent. If you don't even have the commitment to join the team then why should we expect you to have the commitment to deliver content for us?
6) There is one area where an open approach would work and that's the code for the game itself. And that's open. We're not hiding that. It's available for anyone to help us with. Do you see a sudden influx of people working on it? BtRL did manage to pull in a few coders but even with a system where we did say "I need x, y and z coded" we still got poor results. Even though there were no real barriers other than dedication.
So all in all, we've tried it. It didn't work. And we're not stupid enough to try it again.