FD created this game with three modes (you knew this when you bought it), they stated right from the start that all modes were equal and implemented powerplay in all modes, therefore engaging in powerplay in either solo or private group is
not abusing the system as those people are using the system
as it was designed. Now you could ague that it was designed wrong but saying that the people using a feature that's clearly working as intended can hardly be called abuse, you calling it that however can be called just that because you are making unfounded accusation towards a group of player that has just as much right to playing the game as you do.
As for the belief that players should be able to do anything in the game at any time, that belief might stem from
the marketing blurb that states:
Play your way
Experience infinite freedom as you earn the skill, knowledge, wealth and power to stand among the ranks of the Elite.
I could of course be wrong.
Now you PvPers chose to use the
least effective way to engage in powerplay, if all you wanted was to win you'd be better off going the PvE route however you don't and regardless of your reasons you will now have to work harder to get things done.
As for the influence people in Solo and PG have; Sandro has clearly stated that a significant majority is playing in open so the effect the other two modes have on powerplay can't be that great unless of course an organized group decides to start an offensive in either Solo or PG and even then they could still be countered effectively
from any mode by a larger group doing engaging in the same activities as the opposition.
Oh and if for some reason you think the PvE community is deliberately sabotaging PP from modes where you can't get to them, I don't think anyone cares enough about you to even bother.
Losing in powerplay? It's because:
1. You're using the LETA (Least Effective TActic)
2. You're outnumbered.
3. You outnumber the opposition but they have opted to go all in on PvE.
If you want to win; do what they do.
If you want to have fun; have fun
If you looking for easy targets; easy targets are NOT looking for you.
Blaming other players for playing the games as it was presented to them is not going to solve anything, if the powerplay community universally agreed that "hiding" in solo or private groups was unfair there would be no problem.
Random, unorganized players engaging in PP just for the rewards are not going to have a meaningful impact unless FD failed to add a decent level of inertia to the system in which cased they can hardly be blamed for what is essentially a design flaw.
Now I'm sure there are ways to solve the "powerplay modes" issue in a way that doesn't involve taking content away from certain players but it will require a more constructive attitude from
both sides and who knows we might even end up with something that's way better than what we have now without alienation one group or an other. However claiming that you, and only you, are playing the game as it is intended is going to meet with resistance every time.