The Conductor states that "We protect them and nurture them" in reference to the elders... why do that when you could probably eradicate them instead?
Sort of explained at the end of the short story. The ancients' immortality is ensured by the human flesh (they are themselves degenerate humans), and said immortality is needed for them to continually serve the Eldritch Abomination they made a deal with so New York would prosper. It's also implied that similar deals were brokered with similar abominations at the site of every major city in the world. Even yours.
And beyond that - why human flesh? Is there suddenly something wrong with beef/pork/chicken or any other type of meat?
Which doesn't, in itself, explain why they need to be immortal in order to serve the whatever-it-is. Mahogany certainly didn't get immortality out of the deal; indeed, him getting old is the main reason he screws up enough to get himself killed in the short story. The Elders claim they have to be cannibals, but there's no evident reason why their role couldn't likewise be filled by consecutive generations of mortals: they, personally, just plain don't want to die, and are making up excuses, same as the Elder spokesman in the story denies liking human flesh while drooling over a corpse.
So at the end, Leon goes to work for the Elders... why, exactly? What part of anything that's happened makes this seem like a good idea?
In the original short story, he directly meets the Eldritch Abomination the Elders work for, which drives him insane with a mixture of terror and instinctive drive to worship it. It breaks him so thoroughly that he is incapable of doing anything else. It even ends with his now loving New York when he used to despise it.
If the Gods need human meat as a part of the deal with the humans, why they don't just use human meat from criminals or bodies of people that is about to die in hospitals/ dead bodies from morgues? Killing random people on the Subway seems to be a questionable choice
They probably do that too, but only so many criminals and hospital corpses can vanish before they need to do something else. Though perhaps if they took the corpses of people set to be cremated and replaced the ashes...