I do not mean to be insincere, but why would the government or anyone else for that matter directly pay the victims of a natural disaster $500,000?
I can understand a large amount of money being diverted by the government or charities to help the victims recover, either physically with homes or psychologically with mental health services.
Power. The disaster had a human component of insufficient preparation, with Fukushima being the most famous part of it. Letting the government maintain control over relief funds can very easily turn into extortion: "I have this nice house. You could have it... If you told all these nice journalists there was nothing more we could had done."
It doesn't necessarily have to be the intention of the government. A badly traumatised person is hypersensitive to danger, and will perceive everything in terms of possible threats. But also, Japanese culture does seem to put a lot of value in saving face and loyalty to the superior, so a bureaucrat might experience a conflict of interests and misjudge, perceiving his duties to include things they don't.
Also, having money lets people to reintegrate to the economy, while having access to aid services doesn't. Poverty and trauma are a bad starter combo for rebuilding your life.
It takes time and effort to heal, not necessarily money.
It takes time and security to heal, and that includes financial security. As long as you have to divert all your energy into ensuring basic necessities, you will at most cover over the scars. And untreated trauma is a nasty thing: it twists your perspective and leads to irrational behaviour. Apart from this leading to personal tragedy, having hundreds of thousands of irrational people in a stressful situation is a recipe for trouble.