Relevance of Joe Chill to succession of Batman?

Question

From The Big Bang Theory

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Sheldon: I am asserting, in the event that Batman’s death proves permanent, that original Robin, Dick Grayson, is the logical successor to the Bat Cowl.

Stuart: Ooh, Sheldon, I’m afraid you couldn’t be more wrong.

Sheldon: More wrong? Wrong is an absolute state and not subject to gradation.

Stuart: Of course it is. It’s a little wrong to say a tomato is a vegetable, it’s very wrong to say it’s a suspension bridge. But returning to the original issue, Dick Grayson became Nightwing, a superhero in his own right. Batman 2 has to be the second Robin, Jason Todd.

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Later

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Stuart: I’m sorry, but you’re obviously stuck in a pre-Zero Hour DC universe.

Sheldon: Of course I am. Removing Joe Chill as the killer of Batman’s parents effectively deprived him of his raison d’être.

Stuart: Okay, you can throw all the French around you want, it doesn’t make you right.

Sheldon: Au contraire.

Stuart: Plus, you’re forgetting that the Infinite Crisis storyline restored Joe Chill to the Batman mythology.

Answer 1

Sheldon ignores any continuity that doesn't feature Joe Chill

What's going on here is that Sheldon has made some statement about the "Batman line of succession" that ignores events that happened or (more likely) characters that were created after the Zero Hour crossover event. Note that this cannot be his excuse for ruling out Jason Todd, since Jason debuted in 1983, whereas Zero Hour happened in 1994. He most likely is using this to exclude Stephanie Brown or Damian Wayne, since they became Robins post-Zero Hour.

Stuart calls him out on that:

Stuart: I’m sorry, but you’re obviously stuck in a pre-Zero Hour DC universe.

Sheldon believes that talking about events post-Zero Hour is a bad idea, since if Joe Chill had not killed Batman's parents, Bruce Wayne would never have become Batman. Thus he claims that his original argument for the line of succession holds, though admittedly by ignoring the comics he doesn't like.

Stuart contradicts him, pointing out that since Joe Chill has been restored to the Baman continuity by Infinite Crisis, Sheldon has no excuse for ignoring Robins post-Zero Hour.

Stuart: Plus, you’re forgetting that the Infinite Crisis storyline restored Joe Chill to the Batman mythology.

Answer 2

It plays no role in which of the proteges would take over the Mantle of the Bat in the way they are mentioning it.

Joe Chill was not removed from continuity rather that Bruce found who the murderer is was and you're simply linking up 2 different arguments as if the show was at all coherrent when all it's doing is mentioning relatively well known facts to make it sound nerdy/geeky.

Batman knowing who murdered his parents could be said as a point as to why 1 protege should have become Batman rather than the other, along with others... Basically Tim Drake owned and ran Wayne Enterprises, is the best detective in DC, is recognized as "The Detective" by Ra's, went through the same and better training than Bruce did, and I could probably name plenty more for why he is bar none is what Batman is thought to be and better. Bruce has talked to Tim about in the past, can't remember what issue and don't want to say that Bruce thought that tim would become Batman in the future. So there is enough reason to say Tim should have and should become Batman without this.

In context of story, Tim took on the mantle only because Dick wouldn't and Tim believes there needs to be a Batman. Dick took on the mantle only because he didn't want Batman to be a thing anymore, but Tim made it clear that it had to be a thing but Dick believed it shouldn't be Tim because no real reason.

Now back to the Joe Chill thing. How could this relevance? Simple. The relevance comes not from Joe Chill as anything important, but rather in the reaction to how the successors and Batman react to knowing their parent's murderer.

Bruce tracked Joe down, solved the case and depending the sources did anything from stalk him, reveal his identy, to nothing at all.

Dick reacted with trying to kill him, though young at the time so it can be excused. He has since stalked and been a thorn in his side as long as he knows he's alive. It could be argued that Dick moving to Bludhaven was to always be there overlooking Zucco.

Tim reacted with setting up an elaborate series of events that could have killed Cpt. Boomerang, but stepped in and stopped it, before it did kill him. In the issue where this happened Bruce tells Tim that he did the same thing to Joe. Tim also didn't want revenge on the voodoo priest for killing his mother, but I think that was because he was already dead, so not really fair to go off that.

This is the only relevance and I think Tim hunting down Cpt Boomerang and tormenting happened after the fact, so it's a moot point at that.