“A woodpecker is killing my tree.” Really?!
Squirreling away a bunch of acorns The ordinary Blue Jay that we see in north Texas can carry several acorns at once. One or two (or more) in its bill and throat, and at least two more in ”built-in shopping bags” in the form of expandable pouches at its throat. The jay carries them away and hides them for later - just like a squirrel. (forgotten nuts, clearly, are responsible for much of our forested lands)
He stashes between 3000 and 5000 acorns and other nuts per season, some of which may be forgotten about, and grow into big trees. The bird might cram them into a crack in a tree’s bark, or bury them in the ground. That’s not counting the ones eaten on the spot.