Zach only had to retrieve one material, unlike the others who had to do several. It had nothing to do with the fact that he was strongest, in charge, or lazy. It had everything to do with the fact that it was the most difficult and dangerous one to get.
The others were difficult to acquire, mostly due to their rarity and scarcity.
The Thrice-Cleansed Thousand-Year Poison Marble was difficult to acquire because the only places a Poison Marble formed naturally were areas filled with lethal poisons and toxins to the point where most humans died before they could even taste the air.
To Zach and his barriers, that wasn't a problem.
But poison and marbles weren't the only things in those areas, especially not in places with dense enough poison and long enough history to make a thousand-year one. Monsters that were more poison than monster lived there and thrived on the poison. They would get in the way.