The influence borders show you the outline of the areas you control - it would be useful to see how strong that control is.
For example, on the fringes your control would be weak - but with neighbours, it would be useful to know HOW weak, and how strong their influence is.
Out in the wastes, you can often control huge areas of vacant space. It'd be nice to know how strong - or not - this control is, since it's often possible for a single new planet to cut a huge area from your influence.
When planning attacks, it'd be nice to see the spread of 'influence strength' from planets and bases. This would allow you to target influence wars, avoid captured flipbacks, etc.
Basically, an option to fill your influence area with your colour, more transparent or more solid depending on the influence in that square. At a glance, you could then see the influence centers, the areas of influence 'push', and the areas where influence is weak.