Tomorrow I am going to the doctor for the third time for the same problem. Should I ask him to charge me half price because the earlier treatments didn't work?
How does your suggestion for price limits support your earlier stated desire for a free market in the legal profession? There is already a free market. If one lawyer's fee is too high, you are free to find another lawyer who's fee suits you more.
As for your doctor analogy, so long as the treatments are working step by step, they deserve what they are being paid. If, like lawyers, the doctor just screws the proverbial pooch and FAILS HIS CLIENT, there's this thing called Malpractice!