Apart from being alkaline which is a good way of killing germs, ash is a good scourer and it can be used in the kitchen to scour utensils. It does not leave residues when rinsing therefore uses less water and soap saving on costs. Its a very efficient remover of grime and fat. What do you use?
I use detergent gel made specially for washing utensils. It is much cleaner and easier to clean oily stains and grime. However, I still remember my childhood days when ash was the main product that we used to scour the utensils with. But it was very difficult to clean greasy stains using ash and nowadays, getting ash is quite hard.
We use an anti-bacterial dishwashing liquid and a sturdy scourer and they're very effective against grease, grime, and sticky residue on pots and pans. The OP's post reminds me of the good old days when my grandparents used firewood for cooking. I saw how they made use of the ashes to clean the pots as well as the sink. Nowadays, although some dishwashing liquid are inexpensive, some people save more and earn extra by making their own dishwashing liquid using a forumula provided by the seller of the raw materials.
This reminds me of the olden days when my grandmother would get ashes from the firewood to use in cleaning the bottom of pots. When you cook using firewood, it blackens the bottom of pots and pans. The best cleaning material is the ashes from the firewood. However, you still have to use dish soap for the final cleaning.
I also use an anti-bacterial dishwashing liquid instead of looking for such sources to clean my utensils.