See, I look at this a completely different way. For me, the way Begins did it conveyed that exact message, that the problem is something bigger than Chill himself.
Because he was caught, jailed, and killed, it put less importance on the man himself in relation to Bruce's mission. Bruce doesn't even start until after Chill is dead. That says, to me, that this is not a mission of vengeance, but a mission of peace and restoration to prevent any children from experiencing the same tragedy. Some people have always had this theory in mind that every night, in his mind, Batman is fighting "Joe Chill" - looking for a sort of symbolic vengeance. In Begins, it's pretty clear to me that Bruce has "moved on", for lack of a better term, from the single man. That makes his mission all the less selfish.
This is the problem though, in
Batman Begins, he isn't fighting "Joe Chill" at all. In fact he only seems to fight those that create Joe Chills; Falcone, Scarecrow and Ra's Al Ghul in this particular instance.
This Joe Chill is painted quite sympathetic, as if we aren't supposed to hate him, but rather the people who created him. Aside from Falcone's men, Bruce never seems to take an active role against "lesser" criminals in Begins. No taking out crooks looking to rip off some old lady like in "Batman: Year One". Or perhaps my most perfect example "Appointment in Crime Alley". We see Batman primarily going after Roland Dagget, who is a cause of flith and corruption in the East End slum, but also stopping a disgruntled resident who Dagget pushed to the edge. In both cases, against both adversaries Batman seems to draw no distinction between the underclass common criminal and the upper class corrupt businessman. But in
Begins he does.
Thematically that distinction he makes is a sensible one, because considering his past with Rachel Dawes and Joe Chill he views crime as a top down war: cut off the head and the body withers. Unfortunately this is not Batman, and this actually stiffles his character. In
Begins we see Batman go after men we know are bad, we know are corrupt right from the beginning. In most canonical Batman stories we see the opposite; Batman hunts down the petty criminals of Gotham and uses his detective brillance to work his way up the latter unfolding the many connections. In "Year One"'s case it turns out to be a connection between the Falcone's and the police themselves.
Begins ends up with a Batman for whom the villains are much more specific. Falcone needs to go, because he creates "new Joe Chills everyday", Ra's Al Ghul needs to go because he wants to microwave Gotham, and Judge ***an needs out because he and the Arkham doctors are letting criminals get free walks. This is not Batman though, Batman fights everyone, that's why Joe Chill can't get caught.
Joe Chill is an ambiguous criminal, he could be a mob boss, a petty theif, a serial killer, a disgruntled employee or even a desperate poor person....it doesn't matter though, Batman will hunt them all because they all cause destruction and chaos in his city. This Joe Chill was specific, and had a specific and outlined motive for his crime. It takes away from the senselessness, and ultimately took away from the character of Batman, who is supposed to be dedicated to fighting crime since day one.