Hate to say it, but you're all wrong, sort of. Ash is actually a very good, albeit low grade, fertilizer. It has been used for centuries to help crops grow and flourish. Ever notice, or read or see on the news even, after any type of major fire catastrophe, how the growth that comes afterwards is super lush and healthy. Ask anyone about how much healthier and thicker the forests were after Mt. St Helens erupted years ago, or even the California hills after the yearly fires there. Yes a lot of the new growth has to do with the heat opening seeds and the fire opening up the canopy, but plant ash, wood ash, is actually very useful as a fertilizer. I wouldn't be dumping a lot in your grow, but a little bit scattered over the soil before watering definitely does help. Anyone who disputes this, look it up.
Edited this to save you all the trouble:
In the 18th century, the benefits of ash-derived potash, or potassium carbonate, became widely recognized. North American trees were felled, burned and the ash was exported to Great Britain as "potash fever" hit. In 1790, the newly-independent United States of America's first patented process was a method for making fertilizer from wood ash (U.S. patent number 1: "An improved method of making pot and pearl ash)."
Cheaper sources of lime and potassium eventually killed the commercial market for wood ash, said Sullivan.
For the home gardener, however, wood ash can be a valuable source of lime, potassium and trace elements.
"Since wood ash is derived from plant material, it contains most of the 13 essential nutrients the soil must supply for plant growth," said Sullivan. "When wood burns, nitrogen and sulfur are lost as gases, and calcium, potassium, magnesium and trace element compounds remain. The carbonates and oxides remaining after wood burning are valuable liming agents, raising pH, thereby helping to neutralize acid soils."
Where soils are acid and low in potassium, wood ash is beneficial to most garden plants except acid-loving plants such as blueberries, rhododendrons and azaleas. Use wood ash on flower beds, lawns and shrubs.
The fertilizer value of wood ash depends on the type of wood you burn. As a general rule, hardwoods such as oak weigh more per cord and yield more ash per pound of wood burned. Hardwood ash contains a higher percentage of nutrients than ash from softwoods such as Douglas-fir or pine.