According to my chemist (in the oil business) contact, ash is relative to detergent levels in oil. High ash = high detergent. The benefits of high detergents is apparent - extended drains and cleaner engines overall. Detergents help combat acids and moisture.
Ash, itself, is said to cushion valve to valve seat making for longer valve life.
In older (worn) engines, where more oil is getting into the combustion chamber via rings and valve guides, high ash oils can create more deposits on rings, sparkplugs, and valves.
Take a look at diesel specific oils. They are very high in ash content. Simply put, diesel engines need a lot of detergents to keep them clean and to run those long hours. Burning diesel fuel produces a lot of by products. This will change with the new generation diesel engines, fuels, and oils.