You are confusing the application / purpose of seed washers. This is for long-term storage (10-20-50 years), and paper is for short-term storage (1, 2, 5 years). If you are aware of the difference, then everything will fall into place in your understanding.
I'd argue that, under normal circumstances, both last more than a lifetime. But indeed, metal feels tougher 
Also, don't forget that the ink used to write on the paper can surprise you. I have some horrible stories about that. Paper was intact, the ink was barely visible on the sheet of paper.
Anyway, the seed should be checked every few years. These things do not happen suddenly.