Especially since Jesus was crucified in the garden (John 19:41). A garden of death, a tree of curse becomes Eden renewed (John 20:15). The very tree of life.
Can you imagine 'cross' necklaces that took this to heart? Very interesting..
UPDATE: Some artwork along these lines.
Apse of San Clemente's upper church, Rome. Photo: Lawrence OP
Pacino di Buonaguida's "Tree of Life". See here why there's a Pelican at the top!
But of course these superimpose the cross on the tree of life. I can't find any artwork of the crucifixion that has Christ simply hung on a tree! Can you?