This does not solve it. Consider little guy suing mega corp. Little guy's costs may be covered if he wins, but with only 50K to spend, he still could lose because mega corp can drop 5M on the case. This could even make it worse, because without the ability to recover costs, little guy has a small chance at victory and losing the 50k and a large chance at losing the 50k with nothing. With the loser having to pay, it changes to little guy having a small chance at victory and losing nothing and a large chance at losing 5M + 50K.