...the Background Simulator also has a competitive aspect of it in its nature. The way the player interact with Minor and Major Factions is apparent as you help them (or harm them to prevent them from expanding) and they in turn, expand. By nature, this sort of game mechanic is competitive and conflicts it within the all three modes, in my personal opinion is The competitive bit should be in Open Play so they openly compete...
You're still competing with other players in terms of your effect on the background sim if you're playing solo - it's just less direct in that you will only ever encounter direct opposition from NPCs.
Suppose there are two groups of players. One wants to increase the influence of a local minor faction and take over system control for a different major faction. The other wants to maintain the status quo and keep the system aligned with its current major faction.
In the first group, Arthur and Brenda are playing in open, Charlie, Dianne, Eric and Fiona are playing in PvE groups and George, Heather, Ian and Janet are playing solo.
In the second group, Amanda, Bill, Catherine and David are playing in open, Elizabeth, Frank and Gabrielle are playing in PvE groups and Hector, Iris and John are playing solo.
Following what you propose the first group is outnumbered 2:1 but that's unfairly penalizing 8 players for the benefit of 6. With 10 players on each side it's still an even match. You are considering "competitive advantage" only from the standpoint of direct confrontation between players but that's not all there is to achieving ANY goal in ED, never has been.
If you and I were both traders working for opposing factions, if I'm a better trader than you are I'll gain my faction more influence by making it more profit - even without considering any trade missions at all. We're still in competition with each other whatever mode either of us plays in. Similarly if you and were more combat oriented and decided to support our chosen faction through piracy of the oppositions vessels we would have exactly the same opportunity to damage the opposing factions influence as each other - if I were not to be up for PvP action I could spend my time boiling the oppositions NPCs in a private group or solo, while if you were up for PvP action you could still do the same in open, you could boil as many NPCs there as I do in my PvE group PLUS you get the opportunity for PvP action as well. If you
choose not to do that but only go looking for PvP action then it's your choice that limits the effect you have on faction influence compared to mine, not the game mechanics. That's fine, play it however you have the most fun, but if that is not the most optimal strategy for maximizing your effect on the background sim that's not the games fault.