Thank you for the comment and idea!
I've looked at biters drop ore. Please bare in mind I'm hardly a Factorio modding expert... This is achieved in via control stage scripting, which I don't really know well at all. I does look reasonably trivial to make biters drop arbitrary loot (including or exclusively a randomized amount of ash).
However, what I don't know how to do is to detect a biter's cause of death, i.e. only drop ash if they died from fire damage. There is probably a way -- hooking a script in that triggers when a biter catches fire that then checks each tick for whether that biter will die and drop ash if yes. But I don't know how to do that, and that method does not seem like it will scale well with large combats as it would be bad for UPS.
Another complication is: if you wanted different ash drop rates per biter type, then supporting all the mods that add new biters becomes a large task.
It would be cool, though. Also, if biters drop ash when the burn, trees -- the real enemy -- certainly should.
I doubt I'll be implementing this, but someone else is more than welcome to write a mod that depends on this one to implement the idea.