So there are actual poems that embody the ideals of Poetry (capital P.) Most poems will not. Who gets to decide which ones they are? Nobody and everybody. That is to say, I won't argue with you if you have a different set of poems that do it for you or think mine or lousy. I will argue if you think that almost every poem you read does it for you, or if you have never felt it at all. If you've never felt that with a poem, then you have no business in the conversation at all. It's none of your business.
My professor Claudio Rodríguez (also the poet I wrote my dissertation) would say simply that there were whole centuries in which there was no poetry, or that a certain poet had simply stopped writing poetry (while still writing things that looked like poems on the page.) He would use the example of Jorge Guillén. Poetry is not "vitalicio," he said. You aren't appointed for life. There is a hilarious poem by Guillén about some loudspeakers at a picnic. It is very bad though technically competent.
Suppose there was a small midwestern town with four Chinese restaurants. I could say I don't like them, and someone would say, "oh, you don't like Chinese food." No, I do like Chinese food, but I do not like these restaurants. However, to say I like Chinese food there must be some Chinese food somewhere that I like.
Poetry ought to be something like a skill, that can be learned. Then poets would get better and better at it and older poets would write better than younger, since this is not a skill that declines like athletic speed or manual dexterity. You can get better at writing poetry, but you can also lose it.
You could also lose the ability to respond to poetry. I think responding to poetry is also something that you have in a rather mysterious sense. Suppose you felt indifferent (as I do faced with poetry I feel to be good but not great), but faced with poetry you know everyone oohs and ahs over. It is not just the Chinese restaurants in town you don't like, but those in San Francisco.
A more talented reader is probably more receptive, more responsive than I am. They will have more poems and types of poem that give them that poetic frisson. There are people who claim that music by the Marsalis brothers gives them the same frisson as Coltrane or Bird. It is good to be as receptive as possible, but you can't fake it. In other words, you shouldn't pretend that something is poetry for you if it is not.
In a class I gave, I had students translate (many years ago). A student brought in poems by a guy who taught in the English department of the same university. These poems wouldn't work for translating, because they simply did not have enough substance. The questions you might ask about the relation of the translation to the original would not work, because the premise of the questions was the attribution of a certain value to the original.
The frisson is a kind of thing that "catches" in your brain, like a musical phrase that you have to listen to over and over again.
This being said, the type of person I can learn from is often someone who thinks differently, not someone who agrees the most with this theory of mine.