I'd suggest a lot of what is going on Elite is not really as intended, but simply where we've currently got to...
If you consider a Powerplay task, it is invariably easier in SOLO than POWER (at least at the moment) as NPCs tend to not be as challenging as CMDRs. As such, if a group of you are out to achieve a goal, why not choose the safer and more effective method of doing it in SOLO rather than OPEN then? The game is actively rewarding individuals to take the SOLO path. I'd suggest this is counter productive! At the very least this issue needs to be addressed in the way totals/outcomes are measured but SOLO and OPEN being totaled individually. And better still, OPEN simply being made more appealing to CMDRs so SOLO isn't a sanctuary from other players, but instead OPEN is a place to enjoy playing with other players (if/when you wish to).
Now as regards, "Who said that Open is the most important mode for Frontier or the one they would like to become the most important?" No one... But I'd suggest if we want any sort of truly emergent interesting mechanics and cause & effect gameplay in the ED universe, OPEN is the place it will most likely sprout and flourish. So penalising players for playing in OPEN (compared to SOLO) isn't a good move IMHO.
To be honest, I don't know which possibility is worse. One that current systems do not work as intended or one that they work as intended. Luckily, whichever is the case, many things work all right and the game is OK in general. We also know there is some new content coming, maybe step by step issues get addressed. Time will show.
As for the game not rewarding players who chose to play it in Open (or any other multiplayer mode actually)... Its multiplayer functionality is very basic and extremely primitive. You can shoot at other players or not shoot at them and that is basically it. You can form a wing, which differs very little from flying without a wing (yes, I know the differences and in my opinion they are negligible). There are no other means of cooperation between players (built in the game itself) and combat between the players is far from being meaningful. These are all skirmishes, with very little attention being put into strategy, logistics, long term planning etc.
That's why I think that either Frontier is more Solo focused or they do not quite know what form their multiplayer modes should take yet. Or maybe they know, but it awaits being implemented.
I don't think that adding bonuses to individual players (like more influence on PP element of the game) is something that would convince people to play in Open more often. I think the way of convincing more players to go into multiplayer modes is adding more options for groups of players to cooperate and share goals. Within the game itself, through the game mechanics, not through the external forums, player associations, word of mouth etc. In other words: to allow group of players to build something together in game, something a single player is not able to achieve on their own.
I agree that Open is the mode that can possibly be where the most fun is, because for many people (including me) it's more interesting to play with other humans. It's just Frontier needs to think about giving players a bit more than wings and voice communication. That is not enough.
As I stated previously, personally I wouldn't mind them introducing many changes to Open, such as, what many suggested, secure and insecure zones etc. But on the other hand, there are also people who enjoy Open with full on PVP and I don't see why they shouldn't be able to do so. Hence I'd support Open PVE as a separate mode. Since we know we are going to have several modes of play, all of them valid, all of them happening in the same galaxy and having influence on it, that sort of solution would be giving players more options to choose from. The issue is similar to every other issue with Elite: give people something to do, in case of the multiplayer, together with other players.