PvP games take a long time to play but you don't get that much electrum and score from them. So it's not very effective to grind PvP for gaining score/electrum.
BUT, PvP is more fun than grinding AI because you are fighting a real person. So it would be nice if we could grind it effectively.
What if we changed this so that in PvP, the length of the game influences how much electrum/score you get (and you get enough so it's worth your while)? Longer games would give proportionately more electrum/score to the winner. This would remove the advantage for rush "score mining" decks so it retains a similar deck mix to what PvP has now. (the goal would be to make it so it doesn't matter how many turns your game takes, you still get the same electrum per minute, as long as you win).
It should end up so that you get roughly 20 electrum per minute if you're an average player with a 50% win rate, like you can get farming AI3.