The alkalinity of woodash is something that can be quite useful too!
Since we remove plant material, in one form or another, when we grow-our-own, and use the left-overs from that plant to make compost, and since most plant material is slightly alkaline, this means that our cultivation is not a closed system, and that there is, in general, an on-going acidification of soil, albeit a slow process.
So, a little woodash, as a soil amendment, is a good idea in most vegetable gardens, in addition to its nutrient and trace element benefits.
I found this resource from Western Australia's, "Dept. of Agriculture & Food," which I think explains it well:
https://www.agric.wa.gov.au/soil-acidity/managing-soil-acidity