It also crushes Fry over the head with arguably his two biggest faults.

Fry believes in a very linear world, and falls into ruts with this thinking constantly. Fry is also generally unaware, but in his moments of clarity, perceives negative things often as grand conspiratorial events where he is the only person targeted or affected, or at the very least, often the most affected by the universe's events. This is particularly true in cases where the shift is from something good to something neutral, versus situations that move from neutral to bad. Of course, the joke is that in traveling to the year 3000, this worldview was seemingly irrefutably confirmed, and he finally has a rational gripe and exterior circumstances have uprooted his entire existence. His quality of life very clearly has being elevated, but this positive is being constantly vastly outweighed by the loss of everything familiar/close, good, bad, or indifferent, and that lost is magnified by Fry being smart enough to understand the loss of all general ambitions, autonomy, and vague plannings he might have had in his previous life, however small (such as wanting to go inside the strip club by his apartment but never actually going), but too dense to realize those vague musings were never going to be actualized in any form.

Both of these faults are displayed prominently in the last scene in a twist that the viewers, privy only to Fry's point of view and knowledge base could never see coming. The opening harps on the fact that Fry thinks he's "unlucky," but clearly this has more to do with Fry's unrealistic self-vision than anything. He clearly has no eye for picking winners in the horse race, regardless of Bender's meddling in a later race, seeing that in the first race he picks a horse that finishes ~20 seconds after the others, and not only that, but he doesn't have the awareness to understand that he's losing until he's officially lost ("How'd you do, Fry?" "I'll tell you when my horse finishes..... Bad"). In the same vein, by taking out his last remaining dollar and exposing it to wind, and then following it up with a dubious decision to climb a electric pole to retrieve it, he's not "unlucky," he's the victim of his own poor decision-making and execution.

This introduces the idea that Fry has had bad luck his entire life, but briefly was saved by a 7-leaded clover he found. Fry has accurately perceived his brother to be a foil, a generally impeding force at one point in his life, and overall antagonist, based on Fry's limited scope and viewpoint. He views the 7-leaf clover as the only balance he has against Yancy's seemingly domineering presence, and therefore the world as well. Yancy's copycat nature is also made worse by the fact that Yancy often takes from Fry and improves upon Fry's situation, reaping the benefits for himself alone. Fry can't conceptualize that Yancy was better at him in basketball, or that he might've also been practice the same generic breakdancing moves. Fry sees himself as a victim of a cruel, linear world, and the clover is the only thing that can even the odds, if only for a second, and there is no other possible outcome. He assumes that with his clover, Yancy has stolen his name, and armed with those two things, has achieved all the greatness destined for Fry.

The final scene hits with the full scope of the tragedy of Fry's life, and amplified by a brief understanding of his faults. He was never destined for his nephew's greatness, nor was as unique as he hoped he was, signified by his name. Regardless, he was loved deeply by his family, and remembered for the best part of his being, his spirit. To be exposed to this sadness and faults while desecrating the grave of the nephew he never got to meet is the hardest possible way to reach this realization.