I made an account to add my two cents on this issue.
Many of you seem to be ignoring what the OP has stated, preferring instead to believe he is saying something else entirely or just focusing on the carebear insult. Let me try to dissect this from where I'm viewing it. Without antagonizing anyone or coming off as condescending in any way.
I'll preface this by saying that I have never played EvE for more than an afternoon. I've played the older Elite games, and have bought the Beta, with the xpac pass. I am very invested in this. Maybe not as much as some of the earlier investors, but still reasonably concerned.
I am all for people being able to play the way they want. But when the game's multiplayer works the way it does, giving players total freedom, you must expect to compete with, avoid, or cooperate with other players. That's just part of the thrill. Part of the satisfaction.
If you are not looking to interact with players (which is perfectly understandable), then singleplayer is there.
However, a player's progress is transferable between these modes, which creates problems without actually adding anything of value besides the flexibility of choosing when you would like to play online or not. But it's that very flexibility which opens up a Dominant Strategy: Do everything unrelated to PvP combat offline, then bring this progress online when you are interested in PvP combat. I can promise you that very few players can be trusted not to exploit this.
But it's not about gaining an advantage. There's two problems. One is more minor, the other is very major indeed.
Minor problem: Misrepresentation of player achievement. If I see an Elite ranked player online with a decked-out ship, should I be impressed? It's possible that he may have taken the "easy" route and grinded through solo play without the fear of reprisal from other players. Yet here he is in multiplayer. There's an inspiration to be had, seeing players further along in their career when they are undertaking the same challenge that you are. With the cross-saves, this sheen of accomplishment will not exist for the players who DO take up the challenge. This is minor since it's a matter of showing off and of arbitrary challenge. But I believe the game would be more satisfying with strictly locked multiplayer.
Major problem: Since the Dominant Strategy is to go into solo and do all of your mining, trading, and other PvE content, you will find far less people doing this content online to interact with. It wouldn't even need to be true that it's more difficult. People will think it is more difficult by the nature of the setup. "I could do this content with danger of being ganked. Or I could just do this content in peace". Fewer will go for the thrill. And as some people would put it "Give the sociopathic gankers less targets!"
If you want to play in a way that is safe from other players ruining your fun, that is absolutely fine.
However, there are also players that want that challenge, and want that same challenge to be held to the people they are playing with. If you insist that the online and solo modes be progress-connected, you are doing nothing for your own benefit in playing the game. You are only taking away from the intensity, immersion, and sense of achievement of the online portion.
Failing that, it may work to have another mode. A locked multiplayer mode, "hardcore" I guess you could call it. Wherein anyone who creates a savefile can only ever use it in that online mode.
I seriously doubt you could object to that. It does not impede on anyone's play style. And you could still bring your solo credits into the open play mode for a taste of multiplayer.
Again, my worry is that I won't see any PvE'ers online unless they are forced to be there. And don't make the argument that I'm just out to gank them. That's not how I play. I'd like to be among them, or maybe help to protect them. Who knows? There's so many possibilities. But if there's no one on multiplayer doing anything except fighting eachother, that'd get tiresome and reduce the possibilities of what can be done in multiplay. It also makes the ganking WORSE, because the population will be skewered toward PvPers. The OP said as much. I think some of you guys are working against yourselves here.
Anyway, that's my novel, hope ya read it.