Or what about if you treated all law practice as a public service making all lawyers civil servants? The government would pay for the lawyers on both sides, but you wouldn't be able to buy access to a better lawyer. You'd have the problem of excessive lawsuits, but you can counter that with forcing the losing party to pay a big fine that covers the cost of the lawyers. You would also have the problem of how to assign lawyers to cases, but here it might make sense to use a lottery system, where you never know which lawyer you're getting.