Laura Kinney isn't as unhinged as the alternate reality version of the man she was cloned from. She's not killing dudes before they actually do anything wrong. No, the woman who's slashing bad guys up as Wolverine has a different psychological tic: she keeps throwing herself into danger without a care. This week's All-New X-Men #4 shows Wolverine recklessly jumping into multiple near-fatal situations. She's being bad-arse; that's what Wolverines do. But she's being too bad-arse and it's causing tension between Laura and her boyfriend Angel.
It's an interesting inversion of the emotional dynamics readers used to see in her predecessor. With Logan, the struggle was striking a balance between his feral killer instincts and the idealised humanity he and the X-Men fought for. Laura doesn't show that same turmoil; she's been acting like everything's just fine and showing that she's hyper-capable. By the end of this issue, that overconfidence bites her in the butt big time.
Having a healing factor doesn't stop you from being foolhardy.