That would be even less in-character. If Babs wants to bust Kate for being a killer, she doesn't have to wait for Kate to kill again; taking her down at this point would be more trivial for Oracle than fixing Helena's parking tickets. Kate's trust would get in the way more than anything. Why allow another death, if stopping Kate's killing habit is an interest of hers? And that's without getting into the fact that encouraging other heroes to fail and be less heroic is not just outside her MO, but basically the opposite of it.
I find it particularly odd from a literary standpoint, too. Babs basically giving Kate free license is just so much less interesting than Babs saying "no, I don't like your methods, and while you're in my city, you're not going to use them," and Kate having to balance access to Oracle's resources and the support of the Bat network (and the cost of having that network actively opposing her) against her sense of justice.