Unlike true insurance, hedges cost very little to implement other than tying up some cash and credit lines - but it does provide a level of stability which analysts look for.
As I understand hedging, while it cost very little to implement (assuming the airline has the credit) it has the very real potential of expensive losses if the bet goes wrong. Hedging locks in the price for the airline to buy, but it also locks in the price for the supplier to sell. If passengers bought several months, in advance, with a locked-in price for their fare, then locking in the price of fuel would be wise, but most tickets are not bought that far out. The hedge might provide some stability to the cost structure, but that's not a good thing when that cost structure is much higher than that of the competition.
More of a true "insurance" which would limit the exposure to rapid increases in oil prices in the short term would be in the use of a proxy asset lilke West Texas Intermediate crude options which has an R-square of around .98 relative to the price of aviation fuel historically speaking. An airline could buy calls with the right to buy WTI crude (but not the requirement to buy) at some future date, as not to take delivery, but to sell the option if the price of WTI exceeds the strike price. That money from the sale would be used to purchase the more expensive aviation fuel, and offset the increased costs.
Options are relatively cheap in the short-term with strike prices well above of the market, but obviously a high degree of risk insofar, that even cheap options run the risk of being worthless with 100% of the "investment" lost. (Much like most car insurance paid annually provides no returns to the "investment" as no claim was made by the policy holder.) With as many options which would be required given the large amounts of fuel burned daily, I think the costs would be excessive. In an industry which seems to live on pennies of CASM, the costs of bushels in relatively cheap options would probably be too expensive, otherwise most airlines would be in the options market for WTI crude.
However, I think a more prudent approach would be to consider call options on WTI crude for some "Black Swan" event where the price of oil soars to $300 a barrel over some exogenous shock to oil supplies, and an option a year out with a strike price of $200 should be relatively cheap.
So Recommends Jester.