It's not just the soil pH , but ashes provide certain nutrients. If your soil is deficient in these nutrients, then they'll help your soil. If you already have plenty, they won't really help it. A soils test could help you decide. That's if you want to get technical. I think in any case a pH test is a tremendus idea. But I don't worry that much about which nutrients are in ashes.
The "old-time" gardens I was familiar with stayed in the exact same spot for decades and continued to produce. I remember spreading ashes in ours when I was growing up. A lot of other stuff went on there too, manure and leaves, for example, but also chemical fertilizer. Mom still plants some vegetables in the same garden. I think the people Dad bought that farm from first planted a garden there in 1935. That garden fed a lot of people and it still produces well.
My garden does not move around. Some plants use up certain nutrients, or they get leeched from the soil by water. Again I'll mention that a pH test is probably a real good idea, but I just look at adding ashes as adding nutrients and don't worry about the exact make-up of the nutrients in those ashes. I don't pile then real deep and try to grow in that, but spread them out and work them in.
Some people burn wood in their garden for the nutrients. I used to but quit. I feel that the fire in there will burn organic material in the soil that I want in the soil. I burn elsewhere and carry the ashes.
I think I'm rambling even more than I normally do, and I know this is not a scientific approach to it. But it is my thoughts.