Damage caps could lead lawyers to cherry-pick cases. Because the cost of going to trial can be very, very expensive, many lawyers are going to turn down otherwise good cases because, even if they spend, say, $100,000 of their own money to get a case to trial, the potential return is so relatively low that it makes no economic sense to take the case. So, many cases will not be pursued because the expense the defense makes one go through cannot justify even the best possible return.
This state of affairs, by the way, is exactly what Big Insurance and the chambers of commerce want. If they cannot prohibit a person from suing, they'll do the next best thing: make it so difficult, expensive and time-consuming that the lawyers can't take the case.