If players didn't lose cash from battles, then people would construct false-god decks capable of beating a small handful of the false gods nearly 100% of the time, and just farm mercilessly. At least, I would. After making enough money (winning enough cards) to upgrade their deck, they could easily regain the score through score-farming level 3/Top 50/pvp. FG's only cost 30 electrum anyway to beat. One upgraded card will buy you 70 games' worth of electrum against FGs, and a single elemental mastery gets you 4 games' worth of electrum.
I think it's fine the way it is. Newbies can't construct a deck capable of EMing every time against a few gods and just grind until they fight one of those. That would allow players to progress too quickly, without having to earn it. I bet a deck with nothing but flying lobotomizers, a few enchant artifacts, and a spine carapace or fire shield could beat quite a few gods by stopping their creatures before they start and killing those with any attack left. Of course, this would only work against gods reliant on their creatures' abilities and/or with creatures that start off with little attack (shriekers, almost anything with growth, etc.) This idea would fail a considerable amount of the time anyway, and all of the time against the vast, vast, vast majority of gods. Without a significant fee, this sort of deck would be exploited.
EDIT: you can't make an avatar, you don't have enough posts yet (ones in the forum games section don't count). You need 200, I believe, to pic a custom one, and something like 30 to pic a picture of an elements card (any card).