Four greatest poets

One of my friends on her blog has asked the question, "who are your four favourite poets?" She has suggested three of her own but as one of them is me I think we can discount that. The other two are Wordsworth and Frost (I'm assuming that's William and Robert, but it's possible there are others). My take on that is I really don't like Wordsworth very much - his good poetry is too twee for me and his bad poetry is almost indescribably bad. Frost on the other hand I admire greatly. He wrote one of my favourite poems, and no it isn't the one about roads diverging. It's this one

Some say the world will end in fire,
Some say in ice.
From what I've tasted of desire
I hold with those who favor fire.
But if it had to perish twice,
I think I know enough of hate
To know that for destruction ice
Is also great
And would suffice.

Anyway, I've spent much of today considering it and coming to no conclusions. I can easily come up with a list of individual poems that I like and by that measure I suppose the poets that wrote them would be counted my favourites but the trouble is that often my liking is restricted to single poems that I know very well. Thomas Gray? Another of my favourite poems is "Elegy in a Country Churchyard" but how many other of his poems can I even name? Off the top of my head that would be none. (Though I've just discovered by googling that he wrote something with the remarkable title "Ode on the Death of a Favourite Cat Drowned in a Tub of Goldfish" - which, truth be told, is nowhere near as good as the title might lead you to believe.)
Wilfred Owen? Well "Dulce et Decorum est" is another favourite. Most of his other poems are also excellent but that's the one that I know, and really are they better than the other War Poets: Brooke, Sassoon, et al.
Coleridge? Well I like "Kubla Khan" well enough but the "Th Rime of the Ancient Mariner" just goes on for so long I've usually lost the will to live before I reach the end of it.

So I have reluctantly reached the conclusion that I can't identify four favourite poets. I'd probably do better at four least favourite poets, but that would just be mean, wouldn't it.