Actually, I've seen both sapsuckers and woodpeckers do quite a job on
Bradford pears. Those Bradford pears were hugely popular for awhile,
and many a nurseryman made a mint off those crummy trees. They are
crummy because: They attract a lot of insects and bugs and are prone
to disease and die-off.. They have very weak wood and often split
apart under a good wind or stress, and they die quickly.. usually in
less than 30 years.
Of course, you can spray the heck out of them and keep the bugs away
but if you were going to do that why not plant a tree that has fruit
you can EAT?