Yeah, but there's ducking responsibility for your failures and holding people to unreasonably high standards and then there's letting someone shoot you -- for what are pretty questionable reasons, under the circumstances -- without comment. Shooting people isn't exactly a healthy way to deal with your grief either, and it's pretty clearly established that, legal justifications aside, this was pretty much Romy's motivation for plugging him. And I suspect Batman, who it's implied is not exactly unaware of what's going on in the MCU, is aware of this.
It's not exactly having unreasonably high standards to argue that shooting people based partially on their own grief and resentment is arguably not a good thing for a member of a police department to be doing. Batman may be a bit of a dick here, but he's not entirely in the wrong.