I don't know if it's just me, but I'm kind of happy he decided to start over again. He's fought a long battle, and while he can't return to the past, he can set on another adventure and find something that he wants to do. In the past, he had his comrades but nobody else, so perhaps he'll find more people he can become close to this time around.
If he had gone around trying to prove his existence, then even after he successfully managed to, then what? He'll be bombarded with tasks and things he's expected to do, and we won't be able to see him freely travelling, since he seems to be a pretty laxed guy despite the possible loneliness he's hiding.