I do like the idea of there being more stuff out there, especially more dangerous stuff. My first run, I found an LP base, and assumed that it was going to be very important in some way, and that lots of other things were out there waiting to extort or attack me. That story mission with the system full of aggressive mercenaries solidified that idea.
I'd like to see things like that. Maybe not respawning, but pick X systems at the start of the game, some of them have Diktat black sites for high-value dissidents (you could blackmail them for money, keep their secret and/or run prisoner exchange missions for rep and other rewards, or try to free the prisoner for reputation and a bounty from the faction that was sponsoring their activities), some have secret Tri-Tachyon research areas (you could buy ships and weapons with high reputation, or raid them for high-end gear and blueprints, but would be attacked on sight at insufficiently high rep), some have Hegemony bases that investigate Remnant systems and cite the player for ignoring warning beacons, and maybe there are some League colonies out there that mine the local system in search of superweapons that will tip the scales (accepting money from the player in exchange for anything that's not of immediate use to them). Could have a hidden Church reformist colony that can be strongarmed into joining the player faction (starting with Luddic Majority and some stability penalty, but on a highly-desirable world), sold out to the authorities, or traded with.
There could be rare supply runs to these systems that a player could follow through hyperspace, but they'd confront the player if he stayed in detection range for too long while outside of the core.