Yeah, but it seems impossible to experiment on the scale that would have happened in nature where there would have been millions of localized "test tube experiments" ongoing for millions of years.

Of course people can, and do, try to replicate early earth environments and self-assembling proto-cells, but I'm not sure how intellectually satisfying any self-replication success from these "designer experiments" would be, unless perhaps done on such a large scale (simulation vs test tube?) that any conclusions could be made about what likely happened in nature - just how specific do the conditions need to be?