I think it is pretty clear that he wasn't against the copy cats because they were "vigilantes" he was against them because that was not the point of why he was batman and he was against a bunch of citizens trying to do what he does because they just can't.
Why is it pretty clear? The hockeypads line? Yes, I agree that they certainly weren't prepared, but that lack of preparation is what leads them to use guns to fight crime, which is not at all what Bruce interned. A big theme in Begins is the argument of vigilante (a man lost in the scramble for his own gratification) and a symbol meant to inspire people. The copycats in TDK are just an extension of that theme and serve as a direct contradiction to Harvey Dent, who is also inspired by Batman but doesn't become a gun-wielding vigilante (well, until the Joker gets involved).
The point was to inspire the PEOPLE to "take back their city from the criminals and the corrupt." He kind of laughs when he is talking about the copy cats with Alfred. "That wasn't what I meant when I said I wanted to inspire people." There is zero evidence before TDKR that he wanted someone else to adopt the symbol.All evidence points to the fact that he wanted no one to do it and that he in fact wanted a city that didn't need a batman. We can all make up these reasons and kind of interject our own theories but the reality is that it makes no sense!
First, Bruce laughs because Alfred had just made a joke: "Why don't you hire them and take the weekend off."
Second, zero evidence? Harvey Dent? Bruce sees him as someone who can carry on the symbol. Even Harvey himself says "Batman is looking for someone to take up his mantle." That doesn't mean that he's going to go put on the suit (and we don't know if Blake will either), it means he's going to become the symbol that will inspire the people of Gotham to take their city back from the criminals and the corrupt. The symbol of Batman in this trilogy is not about pointy ears and a cape, it's about being someone who can inspire a sense of justice in the people of Gotham. Dent can do that. Blake can do that. Masked men with guns cannot.
Blake is just as untrained as the copy cats were. They actually seemed tougher and dealt with a whole group of thugs for the most part. So he is given a nice computer and presumably the bat suit and now he is batman? That was never the point of batman! It just plain and simply does not make sense.
Think back to one of the pivotal scenes of Batman Begins
Ra's: Anger does not change the fact that your father failed to act.
Bruce: The man had a gun!
Ra's: Would that stop you?
Bruce: I've had training.
Ra's: The training is nothing, the will is everything. The will to act.
That's what Blake has. He has the will to act. He doesn't have Bruce's training, no, but the training is secondary. The point of Batman is not about taking out a bunch of thugs in a fist fight, it's about inspiring people. Blake has the will to do that, as shown by the fact that he attempts to inspire the bridge guards to let them pass, despite knowing full-well they might shoot him dead. And more importantly, he has seen that he can't inspire them within the confines the law, as the rules become shackles.