I think one reason why they don't use a truly random system is the seriously limited jump range of the starting Sidewinder. It would be very easy to find yourself stuck in a cul de sac with very little to do.
That said, there are plenty of other places that would make decent starter systems. It'd be nice if FDev could pick, say, 10 of them, distributed through the central volume of explored space, and have new games start randomly at one of them.
Still, I'm speaking as someone who mainly plays single-player. For people wanting to join up in multiplayer with other friends, finding out that you've started in a system 200 light years from where your buddy is would tend to dampen the enthusiasm.