The four drugs they are testing seem to be already developed/approved in humans for other uses so expanding the label is easy, while avigan is still experimental (some limited approval in Japan, but worldwide acceptance not there yet) and would have to go through much more testing before being unleashed at coronavirus scale.

Also not produced at any sort of scale yet, which would limit its ability to be deployed quickly. These others are already in production and most of them cheap and common.

Surely if it's already being used in Japan it's been tested enough to use globally in an emergency.

It's very limited approval, it's not something that's just approved and available to be prescribed to anyone. According to the wiki it's only approved in an emergency (presumably meaning individual, not societal, emergency) because of concerns with toxicity and alll. And countries don't automatically trust other countries to approve drugs correctly - Europe did not buy what the FDA was saying about opioids for chronic pain which saved a lot of lives on Europe. The damage that would come from releasing a half baked drug into the world with terrible side effects would vastly outweigh the benefits of mitigating coronavirus, and that's a mistake you only get to make once.

I'm sure they'll test the drug in the future though, there are likely plans to test it as we speak, and if it works really well there are lots of ways to get expedited approval, especially in a state of emergency

https://en.m.wikipedia.org/wiki/Favipiravir

One guess: it's not a drug which they have the ability to crank up the production on quickly. Some drugs are easier to make than others.