These ideas are meant to tackle a couple of issues:
We often find ourselves fighting pirates rather than the other faction.
It’s much harder to push systems during busy times and an evening of hard o-plexinf can be undone by a solo rabbit plexer during the quieter periods.
First, I suggest that kills by millitia that yield LP should affect the contested status of the system they happen in. This would mean that in busier periods where you are having to fight more, you’d be able to push the system faster towards, or away from, vulnerability. The extra level of reward for kills would need to be balanced carefully such that plexes are still the most significant way of moving the contested level up and down.
Second, I suggest rewarding LP to factions for killing pirates in the warzone.
Giving Influence rewards for PVP kills invites abuse by killing your alts in enemy militia.
Allowing LP rewards for killng pirate players in warzones invites abuse by killing your pirate alts in enemy militia.
Don’t get me wrong, under different preconditions your ideas would be quite cool, but in EVE with the necessity for alts for literally everything these 2 suggestions are too easily exploitable.
Remember you already get lp rewards for killing enemy militia. CCP has avoided the abuse you outline by making the rewards based on value of ship destroyed.
LP reward for killing militia people, yes. But not for mere pirates and no influence gains. Killing hundreds of your alt’s ships for just LP would negate the gains from the LP, but killing hundreds of your alt’s ships for influence and LP gains at the same time is a different story.