Why would you ever spend your last 24 electrum in PvP1? If you get under 24, just grind AI3 for a while to bring it back up. And it is a necessary evil. The only thing limiting the number of people with bad decks in PvP1 is the cost to play. If there was no cost, it would be THE place grind when you're low on money. Why should that place be PvP instead of AI1?
Also, if FGs were free, then it would be way to easy to get money. You don't "deserve" to win through knowledge and a bad deck, and AI3 would definitely not be faster than auto-quitting FGs. Actually, auto-quitting with a deck that can beat 1/2 of the FGs at least 70% of the time already gives more electrum than farming AI3.