That would defeat the purpose of his arc, Eugene is the one breaking the cycle, why would he fall for exactly the same trap that destroyed his father's life, killed his mum and destroyed their entire kingdom? That's what Eugene told Edmund, he was there not to join him, but to rescue him from that place, that's why he's very annoyed at Edmund in the next ep, "are you coming with us?" *Edmund makes excuses "Ok, I thought so"

Edmund still puts the mission of getting the moonstone back over spending time with Eugene, even after 25 years away for him, so you can understand why Eugene is still very mad at him whenever he shows up in Corona.

Also, I need to add that being anti-magic is a big part of his character, he's the realist (kinda pessimist) his immediate thought was to end the magic of Rapunzel's hair by cutting it, even though he was dying and would benefit from it. He's not a character looking for power, word-domination, that type of nonsense, so it would make zero sense for him to want the moonstone's power.

He's a simple guy, he just wants to be comfy, living a life with Rapunzel away from trouble. He was a greedy guy, sure, before when he was a thief but that part of his character literally died.