There are already limits on contingency fee agreements, this would just alter the limits. The only real difference is that in the extremely high judgments, patients get to keep more of the money. Other than that, it doesn't change very much.
The reason contingency fees are already limited is because the goverment offers lawyers certain protections. In a perfect market, anyone could be a "supplier" in the law industry, and the public wouldn't need any fee limits. However, since lawyers get certain benefits from goverment protection, the public also needs protection from collusion. If anyone could practice law, you would likely see contingency fees fall (along with the quality of representation). However, this is why fees are (and should continue to be) capped. Is $75,000 PLUS ALL EXPENSES in a $250K setllement really not enough for the attorney?
I don't like the government deciding how much is "enough." That is a slippery slope you are on.
Not everyone can be a plumber. You must be licensed. Should the Florida Consitution also impose limits on how much plumbers can charge?
I understand that attorneys are not popular, so it makes it easier to justify in one's mind the imposition of price controls.