This issue that purity comes at a cost will apply all the way through the metals needed, but it also applies in the Sodium Chloride space.
Bulk standard table salt is 97-99% pure and cheap - $1/kg can easily be found and lower prices exist for bulk quantities. Its a sub $1,000/t product. If you shift up to Food-grade salt and pharmaceutical-grade salt the purity is about 3N (99.9%). Pharmaceutical-grade sodium in small quantities like 25kg has prices around $5,000/t ($5/kg). Putting the salt through a modest refining process to remove some of the impurities has put the price up 5x.
You can buy 99.99% sodium chloride, but small samples but the example I found below has an eyewatering price around $1,000/kg. Sodium is no longer cheap if high purity is required. I'm sure there's cheaper options and there would be further discounts for bulk quantities but on the 500g price below high purity sodium is a ~$1m/t. Prices anywhere near this for very high purity sodium chloride are not going to create a cheap battery.
(20min delay)