Here's an interesting review of the effects of returning wood ash to forests.

The ash generated as a by-product of combustion, whether for heat or power generation, has potential use as a fertilizer in forest systems. . . The key determinants of wood ash chemistry are the tree species combusted, the nature of the burn process and the conditions at the application site. Wood ash from hardwood species produces higher levels of macronutrients in their ash than conifers, and the silica content is frequently lower. A furnace temperature between 500 and 900°C is critical to the retention of nutrients, particularly potassium, and determines the concentrations of potentially toxic metals including aluminium in the ash. Fly ash, the lightest component that accumulates in the flue system, can contain high concentrations of cadmium, copper, chromium, lead and arsenic and this ash should not be used as fertilizer. The form of the ash at application is important, with loose ash releasing Ca, K and Na more rapidly than granulated ash. Heavy metal, radionuclide and dioxin contamination of wood ash-based fertilizers is minimal and unlikely to affect ecosystem function. The effects of wood ash are primarily governed by application rate and soil type. The benefits are maximized at low dose rates, with possible toxicity from applications in excess of 10 t ha–1. For most forest sites, a single wood ash application per rotation could replace all the nutrients lost after whole-tree harvesting (excepting N). Long-lasting positive effects on tree growth have been observed on shallow peats, in which the humus is slowly mineralized in response to elevated pH and increased nutrient availability. In contrast, wood ash application to podzols is only effective in enhancing tree growth when nitrogen availability is non-limiting. To date, published research of wood ash effects on trees growing in clays and loams is minimal. A lag time for positive tree responses to wood ash application is often observed, and may be the result of phosphorous limitation at higher soil pH. The greatest reported adverse ecological effects are to acidophilic ecosystems, particularly the constituent bryophyte, soil bacteria and ectomycorrhizal communities.

Emphasis added. Farming trees for biomass energy must return nutrients to the soil after harvest to avoid degrading soil. Using the ash generated from burning a harvest for some of those nutrients is sensible. Using only the bottom ash (not the fly ash) reduces concentration of toxic metals, though I wonder if those vendors who mix the two end up with no greater concentrations than were in the original forest, so it doesn't accumulate.

Even better, in my view, would be if the wood was used in CHP pyrolysis systems. They operate at moderate temperatures and so retain macronutrients, and the char residual produced would be even better than ash, though there is some char in bottom ash.