Ah. Well, this thread deserves a more in depth response than I can give it right now, so I'll share just a few observations and opinions.
For now, my remarks are confined only to poems that are written with a definite scheme of meter and rhyme. But, this comes from a general approach to poetry that differs from that expressed in the original post. My approach is to read a poem as naturally as possible with inflection for meaning rather than structure. While the poet does chose the structure of the poem to convey meaning and mood, that will carry all of that naturally without artificial emphasis. That is just how it will sound 00 artificial. For example, if something is written in the good ole iambic pentameter, that rhythm will come through if read naturally without devolving into a sing-sing effect if over emphasized. The same is true of the rhyming pattern. It does not need to be stressed to convey the cadence and feeling of the poem. There may be exceptions, of course, so each poem needs to be interpreted in its unique context. The same can be said of things like alliteration, which I love. Just read naturally, the effect comes through. Line divisions are another issue. but I think the same principles apply. The listener is not looking at the written word on the page. So it is up to the reader to convey the meaning of the words, using the poetic structure as the framework. Again, there may be variations that need a different approach, but as a reader, listener and writer, this is my personal approach to poetry.
By the way, sometimes writers, both of prose and poetry, are the worst readers of their own work.
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