One solution I have seen to this though, is various annotated editions of poems which add footnotes to explain various references, things specific to that author's culture or time period etc. However, while these are certainly informative, they can be a bit distracting from the poem itself.
I believe this sort of expression (of remixing and building upon and expanding or contracting) is good and healthy and artistic and should be considered an acceptable aspect of creative expression. How original is original? The fact that we are using a common language already ties us to a past cultural history upon which we build up the meanings in what we say and write (i.e., unoriginal from the get go).
I think there are certainly varying degrees of similarity that can be seen in different bodies of writing; some closer to the exact words of others. But at the end of the day, how much does this really matter? I'm more interested in human expression, however it needs to be done, than quibbling over who did what first and by how much.
What little money can be had, yes, might want to be protected so that more art can be produced, and maybe fame can bring a mild sort of immortality to reward the struggling artist. But I don't think what compels us to write (or create) is something we do for fame or fortune. I think it's more to do with adding to the fabric of culture and playing a part in the drama of human history.
1. Poetry seems like a medium that is inherently difficult not to plagiarize. Unlike regular prose or journalism, you don't have the room to do gracefully do attribution (e.g. "According to the Times, two roads diverged in a yellow wood") and the shortness of the phrase necessarily reduces the space you have to make something unique.
2. It's great to be involved in an intellectual pursuit, like open source software, where copying and remixing is not only encouraged, but is a best practice.
3. It says a lot about the ephemeral state and nature of poetry that someone could plagiarize Emily Dickinson and Sylvia Plath, in this age of Google, and almost get away with it.
edit: poor wording on my part. I meant more that it's difficult to avoid unintentionally plagiarizing, in that the form of the medium seems to make it difficult to show that you were trying to "remix" (speaking from a layperson's perspective). The examples given in the OP seem to obviously be ripping off, though.
But yes, it also seems from a layperson's perspective that there would be collisions in how things could be expressed...but I'm thinking as a layperson who doesn't appreciate all the ways that poetry can break common rules of language and expression.