I should probably start out by saying that I am just as guilty if not the worst offender of what I'm about to write about. I think a lot of us tend to forget that there is more to Star Wars than just Han and Leia. While in certain stories of course it only makes sense to ignore all other characters because no other characters are needed. But I think a lot of us (definitely me) can sometimes write them like they are in this bubble where nobody else exists. They've got friends, Wookiees, siblings, and yet sometimes we forget that maybe they might actually spend time with people other than each other.
Utilizing other characters I think can even help us as writers. We spend so much time fixated on these two characters that if you do it enough, writing them becomes a lot easier. You start to understand their characterizations, or at least your interpretations of them, and you just sort of 'get' what they would say or do in a certain situation. I know that I've had times where I decided I did have to include another character and yet I found myself having a difficult time making it "sound" like them.
Let's take Luke. To me, Luke is incredibly boring to write. I suppose I could have more fun with him if I were using him in a more light-hearted situation where he could play along with teasing Han or Leia or laughing at their situation, but I haven't really used him that way yet. Mostly so far he's just been that nice brother who is there to comfort or help in some capacity. I don't think his personality really comes through here. I have also rarely done much with Chewie or Threepio aside from acknowledging that they are maybe in the room. I think at some point I need to branch out more!
Then there's Chewie. I think a lot of people have trouble with him. We never really know what he's 'saying' in the movies. We can only infer and sort of wonder what he actually might say in a given situation. The most common ways to write him are as the wise old sage or as the older brother who likes to tease his younger one. I think a combination of these two can work well, depending on the situation. I really need to start using these guys more.
I suppose I did once use Xizor and a couple of original characters here and there, but most of the time I have remained within the Han and Leia bubble.
Using more characters just gives you more opportunity to write a more complete story. It gives the opportunity to see Han and Leia interact with others and see different sides of their characters aside from how they act with each other. It can allow us to see their relationship from someone else's eyes which can also sometimes be a nice change of pace. And it can just make it more of an actual story rather than just a little snippet of their lives.
Obviously sometimes there's no reason at all to add in other characters. But try not to ignore the fact that there are others in their lives (you know, like I tend to do). Don't go out of your way to include other characters, but don't go out of your way not to.
Again, I am probably one of the worst offenders of this, but it is something I intend to work on and I think it's a good thing to be aware of.