You probably know this by now, but what the heck. I don't think EA as a whole is RCT-only. GiveWell is, AFAIK, very randomista. But there are other EA-affiliated organizations that are not as randomista as GiveWell, notably Open Philanthropy and anything with a more x-risk or long-termist focus.
Thank you for challenging the question's assumption, Mr. Miller. Your points notwithstanding, I think you under-appreciate what we have, even though it could have been much better. I hope the tools that I envision would someday help clarify convincingly why not all regimes are essentially the same for human well-being.
Those are first-order arguments, and they are symmetric. Second-order arguments might consider whether the pro-democracy or the authoritarian side would have more use for this knowledge.