There are variants of this that could work much better than the current system used in most western nations.
Today, if I can spend $1K on legal fees and want to sue someone with a $1M budget, I'll just lose. To compete with that, I'd have to pony up $1M up front and hope I win to recoup my costs afterwards.
The alternative model is this:
Step 1) A lawsuit is filed
Step 2) Each party puts double the money they are willing to spend into the "pot". So if you have a $1M budget, you have to put $2M in. The counter-party willing to spend only $1K puts $2K in.
Step 3) The court takes the available funds from the pot evenly to the two participants, giving each one the same amount as the larger "willing to pay" amount specified.
So in this example: The poor guy seeking justice spends gets a refund of $1K (spending a net of $1K) and his lawyers receive $1M from the pot. The rich arsehole also gets $1K back and his lawyers get $1M from the pot.
I'm not saying this is a perfect system, but it would allow poor people to sue rich people and not be at a massive disadvantage.
Which is why nothing like this has any chance of happening.