I don't think we should be even able to influence systems. Not unless they're podunk 100 population places.
I tend to justify this as "players are representative of the wider population". So if the balance of player activity in a system is in favour of the Federation, so is the balance of the 1000x greater number of (abstracted) NPCs. Cause and effect in-universe and out-of-universe point in opposite directions here, of course.
I'm not sure how someone could expect a relatively small group of commanders to change the events of the galaxy.
I think it's one of those things where both the "players can't change anything" and "players have a lot of influence" are right, because they're talking about different scales and types of effect.
Things players can do:
- change ownership of individual systems
- save individual systems from the Thargoids
- get plot-compatible events, groups, phrases, etc. mentioned in Galnet or similar
- set up conditions which Frontier is able to use to start or continue a plot arc
- determine the direction taken at Frontier-defined branch points
Things players can't do:
- establish new (super)powers or destroy existing ones
- determine the overall big picture balance of the Thargoid War
- start new plot arcs
- determine when and on what terms branch points occur
So for example players have essentially full control over whether HIP 23716 "Wakata Forever!" remains safe or falls to the Thargoid advance. But they can't do anything about there being a war with the Thargoids in the first place, or anything particularly meaningful about whether the overall balance of the war sees the Thargoids gain or lose ground.