I'd argue it was because of battery technology. There was a substantial advance at around 2004 by decreasing the diameter of lithium iron phosphate particles. This increased the capacity significantly of LIB's. Then you have a couple of years of commercialization, then you bring it to market at high cost, then manufacturing process improvements drive the cost lower.

Other improvements drive the capacity even higher through packaging innovations and possible manufacturing improvements as well.

I highly doubt it was due to range anxiety. Even the early Tesla roadster could, at most, go 200 miles. That's nothing on a gasoline engine.

The Nissan Leaf does not look that ugly. It looked like your standard hatchback for the time.