BP has too much FS2 content to be a "Spiritual" successor. I'd welcome it as an actual successor, but Interplay wouldn't. The storyline could likely be worked into a standalone, but I think that for a true spiritual successor, we're better off with something new.
My propositions:
Take hints from other space sims, too. Wing Commander had more extensive, flight-sim inspired damage system and actual carrier landings. X-Wing: Alliance had better cockpit interaction and the ability to control turrets. Those could be worked into a modern space sim.
Use Oculus Rift and related tech to a full extent. In general, take hints from flight simulators with regards to cockpit interaction. It should be completely optional, but done right, it could add a lot of immersion. If budget permits, go for DCS-like cockpits with a lot of unnecessary buttons to press. Manual startup sequences appeal to certain sort of pilots, though again, this all should be optional.
Easy to learn, hard to master. FS2 got that perfectly. I'd say, go further in that direction. Don't overcomplicate weapons too much, but keep them challenging to use. One should be able to just pick up a ship, press a button and fly, but to master it, some training should be needed.
Out of cockpit interaction. This is another thing to learn from Wing Commander. Interactive cutscenes at the very least, maybe even a full FPS mode, allowing you to walk around the ship and talk to characters. This was one of the best things about Wing Commander, and an FPS mode would open yet another modding alley.
Capship command should be an option from the start. While I don't think it should be in focus, large bombers would use similar functions. Basic crew management system could be present, to give some presence to turret gunners, for example. It should have the groundwork for a capship simulation, even if actually implementing it would be up to modders.
Advanced AI, able to hold out on it's own without constant handholding or tight, rigid mission scripting. That's a big problem with FS2, IMO. Capships, even small ones, are hard to use and pretty much require a rigid script to go with. Fighters only do what they're told in most general terms. A modern space sim of the same complexity as FS should be able to address this problem, the only thing acting like FS2 capships should be carriers and battleships (and even those, when allowed to act on their AI, should act reasonably). Done right, it'd add to mission replayability.
Believable atmospheric physics. In atmo, it should play a bit like an arcade-ish flight sim. The flight model should be easy to use, but distinct from space-based one and realistic (think Starshatter).
Modding. FS2 doesn't need you to learn any programming languages in order to mod it. I'd rather have it stay that way. Scripting should stay, but the groundwork for all kinds of features should be in there already, ready to be used with just table editing.