This is a wonderful idea in theory, but it must be handled very carefully.
Let us, imagine for a moment, that you are playing amazing story blended action shooty game. You are loving amazing story blended action shooty game, the story well written and the characters compelling, the hordes of well written foes, let us say, aliens, move as a hivemind, together, flanking, rushing....when one of them starts tea bagging a fallen comrade.
Your immersion was just dealt such a blow that it could never recover. Every errant twitch or odd movement now shouts out to you as some idiot on the other side of the game ruining it for everyone.
This is why I am hesitant about crossplayer. There can always be someone to ruin it for you. But let us look at this on the other hand....
On a devious note, imagine this : you are playing as a wonderful character you have spent some time in, in a hardcore diablo-esque death is permanent kind of deal. Now, unfortunately, after a wonderfully written and staged drama, your character is captured as a slave to be carted of to the arena. Little do you know, your foes are all the same. Fighting for their characters very lives...the stakes would be high. The game tense....each one giving their all....oh, think of it....
It is for this reason I am both excited and hopeful, yet cynical and careful about crossplayer. Given the right guiding hands, this could be amazing....