I think the biggest impediment to fun in the current build is it's too hard to get a fight when you want one. Finding a fight is currently the only objective, so...
It's hard to find an enemy fleet. The field of view on the interactive system map is very small relative to the usual distance between objects of interest, and the TAB-map is non-interactive. This makes getting to any destination frustrating, especially considering the fact that planets orbit the star realistically (which is neat, by the way). It's even worse when you're trying to track down and engage an enemy fleet because they move quickly. You have to hit TAB, note the fleet's position relative to yours, hit TAB again, take a stab at moving your fleet in the correct direction, then wait to see if anything appears on the screen. When it doesn't, hit TAB again, note the target's new position, repeat.
A simple fix would be to make the TAB-map interactive, with at least tool tips and left-click to set course. I think a better fix would be to do away with the TAB-map entirely and allow smoothly zooming out until you can see the whole system. That would simplify the UI interactions required to get anywhere tremendously. If you are concerned about limiting information on fleet composition (currently you can only see a rough fleet size icon on the TAB-map), you could transition to displaying the simple fleet icons when zoomed out far enough on the unified map. Maybe you could introduce a sensor range and stealth mechanic in the future? It would be interesting if enemy fleet AI with weak sensors had limited information about your strength until you were right on top of them...
It's hard to catch an enemy fleet. They move quickly, and it's worse earlier in the game when the fleets you can handle are the smaller, faster ones. Preying on weaker military fleets to enrich yourself is basically impossible. (Are there pirate transport fleets at all?) At minimum, the intercept command needs to plot an actual intercept course instead of engaging in a tail-chase. I don't have any other immediate ideas for improving this except to perhaps increase the number of weak enemy fleets to provide additional targets.
Finally, an unrelated gripe, which I have already seen mentioned a few times: the station/trading UI needs to integrate the refitting screen so you can easily see your options for changing ship equipment. You could even make it so when you click on a ship hardpoint in this hypothetical in-station refit screen, the list of options would include everything the station sells that fits, too, with the price. You could make all your changes, then hit confirm to buy all the parts, similar to how trading works now. I also think the ship subsystem feature would be cooler if you had to buy or loot those parts instead of simply choosing them from a list.