In the standard price-quality model, suppliers internalize the gains from higher product quality — in this case greater flight safety — through their ability to charge a higher price. When the alternatives are "fly" vs. "no fly," however, enough days of "no fly" mean the end of the firm. That causes the airline to favor flight resumption before it is socially optimal to do so. The safer outcome — not flying — doesn't involve higher revenue, as it often does, such as when the roller coaster manufacturer puts in seat belts to assuage nervous parents and thus boost demand.
The "no-ash-generated-crash" outcome probably involves higher reputational benefits for the industry as a whole than for any individual firm.
On the other side of the ledger, I suspect the regulators won't let the airlines charge market-clearing prices for the first week of resumed flights (so far, airlines are telling people that the next week of flights is reserved for stranded customers). That makes the airline insufficiently willing to resume flights, from a social point of view.
I believe that the first effect predominates here, but that is an intuitive judgment, not based on hard evidence.