Too bad that most missions, both canon and custom made, don't take place in Sol...
Yeah, it would be possible to research the overall background starfield conditions and make a tailored starfield background for each of them. However, I'm gonna make a rude guesstimation here and say that vast majority of the systems are located in relatively similar surroundings as the Sol system - outskirts of Milky Way. You would pretty much see similar starfield everywhere unless you're orbiting a star that is immediate part of something like M13 star cluster.
I don't remember any systems in FS2 that would be part of open cluster like Pleiades or Hyades either. And, even if they were,
it would be better to deal with that kind of environment through the background elements.
If there are some systems whose surroundings completely vary from the "milky way galactic norm", you can do the research and substitute a different skybox for those missions, but I'm really not going to bother doing that kind of research as it will not be worth it. Space tends to be quite similar looking, so unless you get into the Galactic Core (in which case you would see some more stars but probably not as much as you would expect) or into intergalactic space... the amount of stars seen in the background would be more or less the same. Most of the stars we can observe actually blend into milky way fog anyway, and same would happen everywhere in the galaxy.
I guess you could try something like Celestia to move from system to system and observe how the background starfield looks like.
to bad that this search for reality has negative effects on eyecandy.
Matter of opinion almost completely. If you preferred the old starfield, by all means use it. Or make a better new one - I'm not even sure what exactly you're after at this point (see below)... More of the blurry stars?
Bigger stars are considerably plausible for other systems adn really improve the effect.
Arguable to a very high degree - feel free to do the research and show how much the background starfield consistency would vary between systems. I seriously doubt it would be enough to warrant more than one 2048^2 sized texture to hog hard disk and bandwidth...
As I said at the very beginning of this thread, most stars can't be noticed that easily. 
Again, if you have trouble seeing most of the stars in the current mediaVP texture,
there's something very special about your monitor settings, because they certainly show up very well on both my home PC and my parents' home PC. They are definitely more noticeable and better defined than the 3.6.10 beta VP starfield, as you can see simply by looking at the comparision shots posted by Zacam. And they are a far cry from the 3.6.8 zeta starfield..

If you want to increase the amount of stars that are >1px in size, I'm not gonna do it. I have tried a lot of stuff when I was making this starfield, and the end result in the mediaVP's is what by my judgement (and as far as I know, other FSU team members as well) was about the best working compromise between variety and keeping the stars from not becoming annoying blobs.
If you want to increase the portion of the stars that are bigger, by all means feel free to do it. Then deal with the fact that the stars stop looking like point sources of light like they are supposed to -
especially in space - as well as the fact that you see the same stars projected to six directions of the skybox, so if you put something like Orion or Big Dipper or some other recognizeable constellation shapes on the starfield, you're gonna see them everywhere very soon...

But seriously, though, check your monitor settings and driver-level gamma settings... If you can, check things on a different monitor. I don't know how things look on your monitor. I don't really even understand how you're seeing what you're describing, so I don't know if you're seeing the same as I, and thus it's a bit difficult to respond in any meaningful way. Hell, take a photograph of the starfield on your display (keep the view still, no flash or other lights in the room, use smallest aperture and sensitivity settings available, and then adjust the exposure time so that the image is accurately lit) and show that to us if it helps to convey what exactly are you seeing.