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The reason he's wearing the robe is a tribute to Inoki, not to LARP as Inoki, and the reason he's doing the tribute is because NJPW wiped out the history of the old belt for the new one, something Okada publicly disagreed with, and has continued to bring up.
He is just representing NJPW's history which he feels the company has somewhat abandoned. It's unironically based, especially if you're an Inoki/old school NJPW guy.