It's impossible in many cases to identify the source of pollution. For instance, suppose I'm a farmer and acid rain is damaging my crops. The source could be polluters hundreds or thousands of miles away. Proving that any specific polluter was the source of the pollution that hit my farm is simply not feasible.
The tort approach in essence says it is OK to pollute as much as you want as long as your pollution will be dispersed enough so that no particular victim can trace the pollution on their land back to you.
Another problem with it is that cleaning up pollution can be very expensive, so that it would not be uncommon for those polluters who can actually be identified sufficiently to be sued to not have enough money to cover the damages they cause.
The tort approach simply cannot deal with the problem. As Friedrich Hayek (one of the leading libertarian economists) noted in his book "The Road to Serfdom": "Nor can certain harmful effects of deforestation, or of some methods of farming, or of the smoke and noise of factories, be confined to the owner of the property in question or to those who are willing to submit to the damage for an agreed compensation. In such instances we must find some substitute for the regulation by the price mechanism. But the fact that we have to resort to the substitution of direct regulation by authority where the conditions for the proper working of competition cannot be created, does not prove that we should suppress competition where it can be made to function".