Well, you know, I just don't find anything appealing about Byron's poetry. A matter of taste i suppose. My feeling about Keats is that he did want fame and recognition, and the monetary means to have a more secure life. His will simply listed his poetry and some books. That was it. His brother borrowed most of what was left of the small inheritance. My point is that I think Keats was somewhat jealous of Byron and Shelly- on two counts- one they had social status, money and women; two, he instinctively knew that he was a better poet than either.
When Shelley drowned there was a copy of Keats last book of poems open within his coat. Even so Shelly apparently thought little of the odes (he did like Hyperion). So his Adonais was not really founded on his appreciation of Keats the poet. (Wordsworth thought Keats last books of poems to be quite good, but was disappointed that Keats hung with the wrong crowd.) Shelley, of course, invited Keats to stay with him during his "recuperation" in Italy. Keats letter to him politely refuses, but does get those "load every rift with ore" digs in. One could imagine that hanging with Shelley was possibly one of the least likely choices he would ever make, regardless of circumstances.