Strangely enough, the stronger Phantom became, the less often he needed the genes of simple monsters.
In the beginning, Adam needed to collect as many genes as possible to become stronger, most notably when he needed genes to fill the chains around his Lock.
Only after he had collected a thousand neutral genes he could find out where his Initial Monster was. This was a direct path to becoming a K1-Phantom and could actually be done quite quickly.
But, the path to K2 wasn't as fast since there were many different conditions. Collecting artifacts was more difficult than a few hundred genes, and Midnight Crystal was a task beyond all others.
Thus, Adam had already collected the required number of genes for the Key long ago. In fact, he didn't even collect the genes of the monsters he killed anymore, because there was no point in doing so.
