If justice is blind, why should funding matter? In other words, to limit the means of funding would be to admit that your bank balance affects the outcome when the whole point of the judicial system is to achieve fairness.
It's possible for the actual justice system to be fair but to still have unfair outcomes if money can influence who brings cases and who can afford to defend them, especially without some sort of loser pays or frivolous lawsuit system. Say you get hit with some lawsuits lawsuits. In each case, the justice system works perfectly — there's a full discussion of the merits in court and after careful deliberation the rulings were all in your favor. Did you still win if the legal fees were enough that you had to cut back your business?
Yes, I'd start with first-party funding making a difference.
E.g. why have lawyers of higher skills available based on their asking fees? That's like openly acknowledging that people with more money get better leverage on the law and have better representation.
If it was to me, I'd take that aspect out of the legal system. We might value such competition in business, but I sure as hell don't want it there -- it's what ensures millionaires get out with a slap on the wrist for dire offenses and poor people and minorities end up with disproportionate sentences.
Of course this would never fly (too much money to be lost), but e.g. making lawyer assignment random for everybody, or having the state demand a total specific cap on what they can charge that's the same for everybody.
In other words: stop allowing legal representation to be a market where more money buy you better services.
I agree with the concept but all this does is shift the costs. Instead of hiring a lawyer, you hire expert witnesses and private detectives and researchers etc.