The only reason we know about Ea-nāṣir is indeed that he apparently kept the complaints he received in an archive in his house; from the linked Wikipedia article:
Other tablets have been found in the ruins believed to be Ea-nāṣir's dwelling. These include a letter from a man named Arbituram who complained he had not received his copper yet, while another said he was tired of receiving bad copper.
And, as the article also mentions, the whole thing became a widespread meme once it hit reddit, which explains why someone would cosplay as him.
Given the fact that they took the time to write a formal complaint in clay (something that's expensive to do in the ancient world), it's indeed likely that his copper was shitty:
"He sold low grade copper disguised as premium grade. He is a man of low repute, a copper dealer with questionable ethics, who cheats people out of their money."
Or you know, just imagine that review on Amazon with 1/5 stars and way more expletives.
And there were many such complaints that he kept! It makes absolutely no sense that not only would multiple people lie about his copper being shitty by carving expensive tablets, but that he would keep false complaints about himself. The simplest explanation is that his copper was indeed shitty and he found it amusing that so many people complained about it.
I always wondered what the circumstances were that the tablets remained where they were. Was the house abandoned after he died? Did subsequent people who lived there just keep the tablets around for some reason?