I feel like being the first player confers a very important advantage : I win most (or some depending on how high I fight) of my games even when hitting in the top 5 when starting and lose them when being second.
On Hearthstone, being second is compensated by 4 instead of 3 cards plus the mana coin card.
Here, being second is compensated by 5 instead of 4 cards (lower relative advantage) and no mana coin card. Besides, the number of cards is not as much of a problem as it is on Hearthstone thanks to the runes mechanics.
I don't think we should change the card count or the runes mechanics : that would change the working strategies too much, and people (including me) have already invested too much time in finding them.
However, adding a mana coin card to the second player would, I think, be a clear improvement.