Q: I found these on my nineteen-year-old Bradford pear. I am afraid the tree may have to be taken down. Agree?
A: These are shallow holes made by sapsucker woodpeckers. The bottom of the hole is just deep enough to penetrate into the sap-carrying tubes in the cambium layer, under the bark. The sap oozes out for a few minutes, which the sapsucker drinks. It then it attracts insects, which the sapsucker enjoys as well.
Although the holes damage the tree somewhat, I have seen perfectly healthy pecan, maple and magnolia trees with hundreds of holes on the trunk and limbs.
There is no need to remove the tree due to this bird damage.
On the other hand, your Bradford pear is at that age when it begins to self-destruct, dropping limbs unexpectedly. You might decide to remove it just to avoid the inevitable limb breakage.