@TheGreatestSwordsman:
Had Luffy been the one that told Rayleigh that he wants to stay and train instead of the other way around, you might have a good point here.
Actually, I think that's precisely backwards.
[[I]Note: I think this post will address many of your points that Luffy hasn't changed, especially pertaining to the above, but don't want to rifle through the past 5 pages collecting them all. I also propose the meta-question following this post and in light of it: Is change necessary or even good, for Luffy or in general?]
ARGUMENT
Luffy is, in a lot of ways, Nietzsche's sovereign individual - or perhaps even the Übermensch. For some idea of what I'm talking about, you can reference this article by a University of British Columbia grad student about Luffy: http://blogs.ubc.ca/hollyonclin/2014/01/28/the-sovereign-individual-in-popular-culture-one-piece-and-monkey-d-luffy-the-pirate-king/ . If something in it contradicts me, then crap, I haven't read it in a while and that's embarrassing!
Anyway, the point is: Luffy is about action, not reaction. (This is a huge theme in Nietzsche.) Words are pretty much meaningless to him if not backed by action, he by and large doesn't care about the past, he does what he wants regardless of what others want him to do, and he doesn't care about moral terminology as "good" and "evil" are just people's reactions to the actions they encounter.
Luffy is not reactive, generally.
After Kuma, Luffy is still being active. He just wants to go back and get back to it - he doesn't worry about the past or what might be wise but rather continues to do what he wants to do. Let me point out also that for Nietzsche, the man of action is typically (though not necessarily) an irrationalist (not to be confused with being irrational); their decisions do not stem from formal reason and weighty abstract considerations but from their own desires and powers.
After Ace, he realizes that this same thing - maybe worse, maybe not, it doesn't matter - happens again. He cannot act on his will, he cannot protect those he loves, his will to act alone cannot overcome these actions by others. In a way, all his bold words are now meaningless, as he does not have the power to act them.
He reacts to Ace's death, not just momentarily, but thoroughly. Yes, he falls down and he cries after both. But he does not simply give up after Kuma as he does after Ace's death. In the former, he tries to fight, tries to overcome by acting. (The comments about promise-keeping in the above linked article could here be relevant concerning a distinction between his break-downs.)
But the difference is most obvious in Rayleigh offering him training and him accepting. Had he just asked to train with Rayleigh, that would have still been active. THAT would have been a failure to change and develop. No, Rayleigh offers him training, and he thinks about it - he makes rational considerations, reacts to the circumstances of the situation - and he accepts this offer. His acceptance to train is a reaction to an offer to train, a suspension of his normal modus operandi in an effort to be able to act according to his will in the future rather than fail to act his will in the present.
Now he talks about taking down the Yonko. He doesn't say he'll do so immediately, just that he plans to do so, but that isn't an important point at all. The important point is that, through his reaction to Ace's death, his recognition of inability to act his will, and his reaction to Rayleigh's offer, he is now strong enough to act his will. While his bold words in the past, upon Ace's death, were realized to be meaningless in the absence of the capacity to act on them, his bold words are again meaningful since he has developed the ability to act them (at least potentially).
That is Luffy's development from Ace's death. After his crew, he thought he could take action and power through it - get back together and keep going. After Ace's death, he realized his actions and power alone, without regard to the actions and powers of others, could not overcome his obstacles. That is the central distinction between the two cases. He then becomes thoroughly (but temporarily) reactive, accepting and undergoing two years of training under somebody else's direction - accepting that he will follow those directions without failure - so that in the future he can have the power to act his will, to overcome his obstacles through action and power.
The ability to act your will successfully, by the way, is the heart of many senses of freedom, a notion central to Luffy's character and dream - "I just want to be the most free man [read: the sovereign individual]".
From the perspective of activity as opposed to reactivity - a perspective which powerfully aids the understanding of Luffy (his own traits that he has and that his dream will accordingly demand of him, his motivations, his values…) - the Kuma fight and Ace's death could not be more distinct. [[I]Disclaimer: in many ways, I have not here said anything new that hasn't been said in the last few pages of argument; rather, I've just reiterated many of the common intuitions and themes in different words. I also don't think I've entirely refuted anyone's position, but rather hope to have shown that the issue at hand is a bit more nuanced than some positions have portrayed; there here seems to be a bit of truth in at least some of each person's claims]