The high heat in kiln drying destroys the pectins in the cells, weakening them. They do not stand up to repeated vibration well, and will break down faster than an air dried wood. Kiln dried wood has its place in the housing industry, unless you live next to an active Railroad line, or in the flight path of an airport runway! For most home construction, however, such wood is not subjected to lots of vibrations, and it lasts as long as any wood house is expected to last.
The famous Stradivari Violins, made more than 400 years ago, were made from wood stored in warehouses near sea level, where the salt laden air also helped to destroy the pectins in the wood cells. That is why the violins have the distinctive sounds for which they are known. However, they are all beginning to lose their sound qualities, as the wood begins to deteriorate. There is an effort underway to conserve these woods, but no one has found a way to get material into the cells through the cell walls to strength each cell chamber, nor have they found any way to strengthen just the cell walls. Oh, they also found that leaving a violin in a museum display case without playing it also leads to deterioration rapidly. That is why you will occasionally see a credit, say, on a PBS broadcast of a symphony concernt, that states that the lead violinist is playing a Staridvarius violin loaned to the orchestra by some museum. Museum curators are doing this kind of " loan " to advertise the fact that the museum owns one of these violins, and to have it played in public just to get someone to play it!
While the requirements of wood used in gunstocks and knife and Axe handles is nowhere near what vibrations are required of thin wood in a violin, the vibrations delivered to axe handles, in particular, can be very violent, and harsh. That is why using a wood like Ash, or Hickory, which have good lateral cohesion between cells, makes them the choice of woods for these handles.