Down here in Florida the natives at palms fairly often. Saw palmetto also grows like weeds here. You CAN eat the chutes beneath the ground of very, very young leaves, but there is very little nutrition in them. Most of the natives put them into cooked items and removed them after the cooking was done. Mostly they were used as a "Tea" item. Boil out the nutrients and discard the chutes afterwards.

About the only thing you'll get out of most palms in North America worth eating is the heart and grubs.