As both an aircraft engineer and pilot I do feel that so much of what has been written here has been absolute drivel. There are just so many variables associated with the potential for engine damage that I would suggest it's almost impossible to predict.
A good metaphor, understandable by most, would be to compare volcanic ash with potholes in the road. Is a 6in deep pothole bad for your car. Well dependant how many, their dispersion, how fast you hit it, steepness of the sides, etc. etc. etc. One 6in deep pothole on a 200km journey, probably will have minimal effect, whereas a 6in pothole every few yards would. If the sides drop away steeply then it will have more effect than if the sides are quite angled and gentle. The speed at which you hit it will have an effect on potential damage. A 6in deep pothole in a concrete road will probably do more damage than one in bitumen. How many potholes has the car been driven over since last being serviced. Etc.
I do not believe that there is adequate science available to accurately predict damage for every flight undertaken. You need the nature of the ash - silica glass, pumice, water content, etc. their ratios. You need the density of the ash in parts per million. You need the time spent in the ash - whether just transiting a level or continuous flight. You need flight engine parameters - thrust settings, etc. You need a history of previous encounters. You need engine type - some engines may be better able to cope than others. The list goes on and on.
When I flew regularly, risk analysis was considered part of the job, nowadays I suspect less so. And irrespective of whoever you care to blame in the final analysis it's up to the captain to decide whether it's safe or not. What scares people here is, I suspect, an unwillingness to take on that responsibility.