I have a couple of young, tall, skinny trees sprouting up in the yard and in the flower beds that I am going to remove. The trunks are maybe a meter long and half a centimeter thick at the base, so they aren't old enough or thick enough to be thinking bonsai yet, but I have been thinking I could experiment with literati style, maybe bending over 180 degrees. Would you wrap wire around the trunk and bend it all at once or over a couple of years? Bending that much at once seems to be asking it to break, or maybe demanding that it break.

Depends on the species. With pine, juniper I would not worry. With Cotinus however..

Particular species:

One is a cherry of some variety. I have a wild cherry in the front yard and a Japanese variety of some kind, and it could be either one. It isn't big enough yet to have flowers, etc.

One is a sycamore. These are not usually considered bonsai because the leaves are big, but the tree grew out of a pot holding an azalea and grew over a meter last year. It might work. Something bent around with sycamore leaves growing only at the end could win the ugly contest.

Another came up in PlantNet as Chinese Tallow Tree. Somebody planted one in the neighborhood and now we all have them. One of them is two years old, two meters tall, and about a centimeter at base. It might work if I chop it off less than a meter and bend it around.