Are all arguments for "random" based on ignorance?

That's the nature of truth. Everything should be subject to that kind of thinking...no matter how concrete it seems. It's only the best explanation at this time with the current information. The trouble starts when we fill gaps with umptions. It's difficult to NOT make a declaration as to the nature of things; even things we don't know. It gives our mind a foundation(albeit a fantasy foundation in many cases) on which to form some structure; make some sense.