Last year, the Oregon Supreme Court overturned that law, saying in essence it was unconstitutional. This proposed constitutional amendment, referred to the voters by the legislature, would restore and expand the legislature's right to cap such damages.
Most civil suits ask for money damages.
The latter are meant to punish especially egregious behavior and are rarely asked for and even more rarely won. Compensatory damages are either economic or non-economic. Most appeals are limited to procedural issues. Jury instructions and other procedural matters can be and are the basis of an appeal, but not the amount of damages. The judge doesn't set the damages, the jury does.