Be more permanent, though. Arthur you could probably scare off this easily, but Nigma's smart enough to know that a cape can't throw you out of your own house, and if he decided it was worth it to him, could just bring Arthur back and pick up some cops while he's at it (nothing delights a villain like making the cops act as enforcers - it's good revenge and is hilariously infuriating to the impotent capes who they're being legally forced to protect you from).
Babs was really busy, though, you're right. And stressed and annoyed and depressed and all sorts of vexed and unpleasant. If there was ever a time she'd try the quickest, most minimal effort solution first it was probably then.