Imagine a complete solarsystem to dive in to with a star i the middle and planetoid companions orbiting around it.
If you get close to the star your ship is getting hotter and finally starts to get damaged.
Now imagine different classes of stars with their own characteristics such as heat, radiation, flares and gravity. Think of them as a stationary enemy with a minimal safety distance, estimated by your science officers.
I think it would add a very interesting element to exploration missions.
Anomalies (some of them) should exist in close proximity to stellar objects that gave their birth in cases that they are naturally short lived.
So what if you could have shields that permitted you to enter a stars corona a moment to gather data and eventually find exotic anomalies. Personally i would love it compared to the dull anomaly gathering missions we have today
A star (or more than one ) in each system would bring natural lightsources to the systems and emit light from the right direction which it don't in many explorationmaps today.
I like the idea of giving certain stars a little "personality".
You wouldn't have to worry about redesigning a lot of missions to implement this either. Most missions take place around planets in the star's habitable zone which would be way to far out for the star to have much affect on a starship (for example, our sun's habitable zone is from 70-115 million miles out).
So the devs only need to create a few maps for these specific 'close to the star' missions.