If woodpeckers were to get them, “presumably they wouldn’t be around for very long" was National Geography’s (NS) answer to its Weird Animal Question of the Week.
Woodpeckers peck wood for several reasons, for instance “to excavate nest cavities, dig for insects or sap, or create holes to store food.” And they do bang hard.
The short answer, according to Richard Prum, an evolutionary ornithologist at Yale University, is “good evolutionary design.”
The long answer is a bit more complicated. NS mentions that woodpeckers have 1) tiny brains (2 grams or 0.07 oz.), meaning less risk of injury, 2) very brief impact time (0.5–1 millisecond), 3) their skull structure prevents injury (dense bone outside; porous inside), 4) their brains fit snugly into skulls, “preventing the organ from banging around”, 5) the orientation of the brain “creates more surface area to absorb … exacting blows” and 6) “ the hyoid apparatus, a bone-and-muscle structure that wraps around a woodpecker's skull, also keeps the brain safe.”
In his book Creation: Facts of Life, Dr. Gary Parker points out that the woodpecker is a “marvel of interdependent parts or ‘compound traits’ – traits that depend on one another for any to have functional value.”
Dr. Parker suggests that the Darwinian trial-and-error approach would have led to the extinction of woodpeckers. If their wonderful apparatus had not been in place at the start, they would have died off.
NS acknowledges that woodpeckers are amazing creatures: “The woodpecker’s capacity to absorb blows has even inspired a system to reduce concussions in sports such as [American rules] football.”