Richard Posner (of course) has the answer--they're a way for airlines to ration plane travel without raising prices:
Persistent delay is usually the result of a failure to use price to
equate demand and supply. When demand increases in advance of an
increase in supply, failure to raise price results in buyers' incurring
cost in the form of delay rather than in the form of a higher price...
So why are airline prices so low? The answer may lie in the lumpiness
of airline service. ... The fixed costs of modern
passenger aircraft are very high, but the marginal costs--the costs of
carrying one more passenger if the plane is not full--are very low. At
any price above marginal cost, the airline is better off selling a
ticket than flying with the seat empty. Competition between airlines
will therefore exert strong downward pressure on price. Prices tend to
be pushed down to a level at which the airlines find it difficult to
finance the purchase of new planes. As the existing planes age,
equipment failures become more frequent, contributing to delays and
cancellations. Airlines prefer delays to cancellations, because they
get to keep the fares, and they resist raising prices to reduce
congestion because that will make it more difficult to fill the planes,
and an empty seat is, as explained, very costly in revenue forgone.
The best solution, Posner suggests, is a Pigovian tax on air travel, where the tax rate would vary depending on the contribution of the route in question to overall airport congestion. In addition to eliminating the deadweight loss caused by airport delays, this would presumably help spur much-needed investment in high-speed rail, which Brad notes isn't getting any love from the feds. For a variety of reasons, though, this is almost certainly just as much a political nonstarter as road congestion pricing seems to be.