No, and this is, in my eyes, the first and most common mistake, when it comes to this matter. That's also why solo/private players come to these topics to just troll, because w/e, they have what they want, what's the problem?
"Let me be, I'm fine."
No, because we (I) want you and everyone to populate open. So no, a pve server does not only allow people to play their way (it sure does that), but it ALSO subtract those people from the other mode. Where you are missed.
"If you want to pvp, you can just go to open."
Yeah but no, because it's open, it's not pvp arena... sure some people don't behave, but it's mainly the fact that everyone can just *snap* disappear from this mode and go in solo/private at will, that slowly makes it a de facto pvp thing. You can totally PVE in open, with friends, with strangers, alone while minding your surroundings for potential offensive player action. That's what I did all 2015, and it was great.
I guess nobody pirates any more (not that it ever really worked, but...).
Anyway. Please just realize that going in solo / playing your way in private is not just that. Some people do enjoy the randomness that only open can provide, it does require cmdrs of all sorts to be there, and they're not.
Players are not a commodity. They decide when, if and where they spend their time. No amount of "I want" is going to influence them.