The thing is, how would that differ from a local or national organisation whose sole purpose is to provide unbiased investigations?If this is a hypothetical situation where that could be achieved, wouldn't it be better to have it as close to the place where the incident occured to serve the correct sentence/punishment that fits the society/culture of that area?

Unless you're assuming that having it be an international organisation is the part that would make it unbiased in which case I would argue it would make it more biased, giving international powers over other countries, abilities to manipulate the public opinion and sturr up riots etc. See UN.