The fact that it's called an ecosystem implies that there are many factors contributing to this idea, and I think it would be difficult to say that any one of them is the most important. Furthermore, the idea of an ecosystem is a human concept that's being applied to the real world in an attempt to better understand it, but this doesn't mean that nature "thinks" in terms of ecosystems or has any particular fidelity toward the definitions that we've created. This would probably be an easier question to answer if we were looking at a specific ecosystem, particularly a smaller one, or if we were specifically investigating just one portion of an ecosystem.
However, an ecosystem is basically the interactions between living (biotic) and nonliving (abiotic) portions of the environment, so we could reasonably argue that the most important aspect of an ecosystem is the ability for these things to interact at all; that is to say, transferral is probably the most important part of an ecosystem, whether we're talking about energy or matter. Without the ability to move energy and matter between living and nonliving portions of an ecosystem, it would basically be impossible for organisms to acquire enough nutrients to survive, nor would they be capable of acting upon their environment.
One of the most significant examples of this concept involves the early Earth, which had an atmosphere with barely any oxygen gas in it. Over time, due to the metabolic action of bacteria, the atmosphere accumulated a massive amount of oxygen gas relative to its original composition, and that oxygen is now one of the primary requirements for modern life. The significance of transferral in this case was that the oxygen was cycled into the ecosystem in some way; the fact that it left as a gas, rather than, say, being trapped in the bacteria's cell even in death.
Specifically investigating how transferral between and within biotic/abiotic systems is destroyed by environmental pollution is an important question, but it is one that is probably not easily or definitively answered unless we look at specific examples. In fact, total destruction of the ability to transfer matter and energy is basically impossible, so we can really only talk about changes that make it improbable or greatly reduce it. For example, environmental pollution from fracking can change the pH of water, making it virtually impossible for certain organisms to live in that water and thereby greatly reducing the ability of those organisms to participate in transfer with any of the abiotic factors of that water. In a conversational sense, it would be easy to say that this ecosystem has been destroyed, but a more scientific and less passionate approach would simply describe it as altered or negatively impacted by pollution.
In general, we could investigate ways in which pollution;
- physically interferes with transfer by blocking or absorbing it
- alters the effects of transfer by changing environmental conditions