Earlier quoted context omitted.
"Loser pays" would go a long way, I think. Not being that familiar with the US system, what's the reasoning not to have this?
If loser pays, poor people would be discouraged from even attempting to sue rich people. Even if the poor person has a legitimate claim, there is a small probability that the rich person will win with their superior lawyers and the poor person will be bankrupted by the legal fees. Since they will know that from the beginning, they won't sue in the first place.
But it still doesn't solve the idea that the "Law is more equal the more money you have." .