You are correct, you cannot not mimic the mimic…
There is actually nothing preventing you from using Mimic on itself. The text says "Choose a card any monster has in play...". Mimic is a card a monster has in play, therefore it is a valid target.
The problem is that doing so accomplishes nothing (outside of wasting 1 Energy).
What this guy said
Logically speaking, he would spend a mimic to get a mimic. The first one would be used to get the second and still left with one mimic left.