Can anyone tell me why they choose to have the students cut and paste the poems rather than just use a folder and hole punch each poem to be added to the poetry folder?

I think I'll have them cut and paste.

With my students, I have them cut along a dotted line, paste and then illustrate. I always type the poem into a text box so that I can easily move it around, change the font/font size etc.

I would have them paste the poem into notebooks rather than having them copy the poem. First graders are still developing fine motor skills and their hands get tired pretty quickly. If it is a shorter poem, you could have them copy it, but what is the purpose?
I am using poetry binders, so they will just put the poem in their binder, circle word wall words, end marks, capital letters, rhyming words, etc. They will then illustrate the poem on the back. If time, they can recontruct it in the pocket chart and read it to or with their center partner. Their poetry binders will stay in their book boxes so they can also read them during reader's workshop.

I gave the kids a poem based on the sound of the week. The kids would read it and highlight any words containing the sound of the week. I have two books of poems that I would copy from that were broken down this way.

I am planning on having a poetry center this year and using a poetry notebook as part of it. My question is should I have the students copy the poem into their notebooks and then illustrate or give them the poem to paste in the notebook and then illustrate? Or maybe a mix of both depending on the length of the poem? Also any suggestions on poetry centers/notebooks in general are welcome. Thanks!