Chances are good they consider doing just that, then realize it would solve nothing. The info being out here and now guarantees there are backups, plus who knows what contingencies in case it's taken poorly.
Best to accept with good grace, return to friendly territory, then start plotting murder.
Preferably in a way that won't be tracked to them.
Why would they care about Coil's death being tracked to them? If anything, they would be quite happy to have it traced back to them since it boosts their rep and/or shows they uphold the Unwritten Rules.
And no, they don't know if Coil already has their IDs or has backups of them which is why it is best they strike now. Even if Coil did have their IDs and have backup plans to release them, it's better for everyone here (except Coil) that he dies now since it's been proven he a) has information gathering capabilities far beyond what he should and b) is clearly willing to trample all over the Unwritten Rules.
Capes dying in a fight is fine. Capes being unmasked and killed is not. Kaiser even explicitly notes this in his musings about the 2nd time he and Lung met at Somer's Rock, about the "idiot who killed Fleur."
Finding the identity of a kid, a hero who is actively disrupting things, is both perceived as easier and less threatening than doing it to professional adult villains that have played this game for a *while*.
...It's still incredibly threatening, especially to the adult villains in the room. This is a very unspoken threat that he can do the same thing to every cape in the room.
Grue, for example, should be balking at this since he very much does not like breaking the Rules or drawing heat down that him and the Undersiders cannot handle.
Kaiser should've already realized the implications of what Coil did, but here it seems that he ignored every single big warning sign other than the potential backlash of assassinating a cape. Which, imho, is not good writing.
Lung should've recognized it too and, even if he doesn't have as much to lose as Kaiser, more than likely incinerated Coil for having the temerity to do so.
You both seem to think that this is an easy thing to ignore for all involved. It really, really is not.