My territory only consisting of a circle around my systems seems basically arbitrary. Most of the systems that need to be "inside your influence" to get an effect are meaningless because it's impossible to get them inside one of these circles, either because there is no place in range for you to colonize or because it's not worth it to do so given the HEAVY expansion penalties.

Influence area being a circle makes sense if you think of it as the strength of propaganda communication a system is shooting out into space. The more powerful your influence generation is (source strength), the more it can travel through space before attenuating (size of the circle). If you generate enough influence in a system, your circles CAN potentally envelope the systems that you want. Influence conversion also makes sense with circular influence zones (think of it as a nearby system from a different empire is broadcasting propaganda with such strength that when you turn on TV, all you see are how good life is there and want to join them).

Frankly, the whole situation needs to be more cohesive. We should have control over our borders. The way that these work, expanding into empty space while ignoring starlanes and valuable systems, is very screwed up. Even if we don't colonize, we should be able to build starbases or outposts or military bases or something in order to shape and control our space. Our influence should spread along startlanes, not out into empty space (unless the planet is an isolate, and even then it should head toward known systems).

As a real world example look at Russia. Most of Siberia is empty and uninhabited. That doesn't mean it's unclaimed just because it's not within an arbitrary distance from the nearest city.

This is an example of influence through military. On Earth, you have manned borders with some sort of access control. Thus Siberia still belongs to Russia as Russians put a fence around it. You cannot do so in ES2. You only own systems. Anything outside it is not yours. You cannot draw an arbitrary line and say all systems inside belong to me. If influence was a mechanic based on military, star lanes make sense. But star lanes are only preferred way for travel, not the only way (free travel is also available). This means that influence need not spread through star lanes alone. Moreover, if everything was enforced through military (like starbases, outposts, etc), then no one will want to play the other game play styles. Remember that it is possible to win in multiple ways in ES2, and influence is just one of them.

I still believe the above will favour a militarist strategy above all else.