In my last game, I played probably normally (except for raiding New Maxios a lot for blueprints), at first. That is, do missions and kill pirates and bounties for income, explore a bit find a good world, build colony, stay below radar until colony is powerful enough to defend itself, in meantime kill more pirates and bounties.
After I reach the point when I can defeat endgame fleets and my colonies defend themselves, what is next? It gets tiring spending the majority of my time traveling (with burn 20) to kill pirates because core worlds cannot defend themselves, then more time to fix problems with major factions because they refuse to leave me alone, and expeditions are too frequent to bribe away, not to mention paying extortion money leaves a bad feeling. I should be the one extorting them when I am stronger than them and defending their sorry cowardly hides from pirates. (I am not turning off Free Port when I want the growth boost to grow my colony faster. Free Port is nearly half of all growth bonuses.)
I would like to explore more than a few distant systems before I get yet another alert of a pirate activity, pirate raid against core world (because core cannot defend themselves), expeditions, or whatever, then travel about half the sector to fix the problem. It would be so nice to delegate NPC fleets from my faction to take care of problems. NPC fleets #1 and #2, take out those pirate bases. NPC fleet #3, sat bomb Sindria until it disappears from the map because the Diktat will not stop bothering me. Now I can go exploring, doing quests, or killing Remnants.
If I want to use cores to colonize as much of the sector as I can, Hegemony becomes a headache. Sure, I can bribe them away, but because bribing cannot be set to the default response (miss an alert and cores get taken), not to mention it is extortion money (again, bad taste), I like the more permanent solution of eradicating them from the sector so that I do not need to deal with inspections or bribes anymore.