Speaking of straw, your talk about lime kilns is a straw man argument. Nowhere in the article is there any mention of lime kilns.
Then try to get the necessary amount of lime without kilns. Doing it in the open fires is so much less efficient that the amount of fuel required would need to be multiplied several fold. Besides, the pottery kilns had already been in existence, so the crude technology was available - but nowhere near the scale suggested.