What about this: you drag me to court, you ask me X millions in damages; if you lose, you owe me X millions. Now that's a lawsuit I would pay for upfront if I think I'm in the right. Even better: many lawyers would probably fight to get my profitable suit pro-bono so they can cash in a big chunk of the eventual damages I would get.

Actually it's not great since a disproportionate part of the outcome of legal proceedings is luck, just like all of life.