For this to work, we'd need a much different court system.
Suppose a company pollutes, and I want to sue them.
First, what is "fair compensation"? How do you tell if the damage to me is $100 or $200? Is there a list of things I'm just expected to put up with, or a price list? What's a generally degraded quality of life worth?
Second, in order to do this, I need to spend a lot of money up front on court fees and lawyers. I may need to take a lot of my time. If I don't spend the money, I don't get any compensation and the company gets to do as it pleases. If I do spend the money and time, there's no guarantee I get any compensation. If we do "losers pay", I risk a whole lot of money if I do file suit, while the company could well wind up paying tens of thousands for damages of a few thousand. If we don't, how do I get compensated?
Similarly, finding out exactly what's happening can be expensive, and somebody's going to have to pay for it. My lilacs are dying. What's killing them? An expert might find that it's primarily due to some chemical or other, and that expert will charge. Now, is somebody going to tell me which chemicals come from which company without me spending serious money? Bear in mind that lots of companies consider their chemicals to be trade secrets, and this came up several years around here. During a fire at a factory, some firefighters were injured by chemicals they hadn't realized were there, and businesses defended their decision to keep dangerous chemicals secret.
Third, we have to provide linkage between damages and pollutants and polluters at a certain level of proof, and we have to determine what level to use. This is particularly difficult when the causes and sources are mixed.
For this to actually work, we need truly massive government subsidies to courts and investigative bodies, which I've never heard any libertarian recommend. Without these, a company is at liberty to pollute my land without effective deterrent or recourse, as long as they don't do a tremendous amount of damage to me personally.
It's FAR more effective and efficient to have pollution regulations that are enforced by an arm of the government.