I think Loki never really needed to prove himself worthy. He already was better than Thor, he always was. He wanted Odin's approval and the title of the "better brother"- something he could never have. And maybe he just ended up ruining himself over something that was destined to remain a dream. He ruined himself a million little times.
Ps: just trying brush up my English for my exam tmrw. Feel free to point out grammatical mistakes.