P.S. Sorry if this somewhat incoherent, but I just woke up and have not had any caffeine yet.
No worries - it wasn't incoherent.
On the whole I think you've got some valid points. I think there might be other interpretations, but that mostly falls under the category of "Are they convinced there's something to be gained here?" The other gangs might care more if it gives them an excuse to get rid of Coil.. but that requires him to be enough of an annoyance / problem that they are looking for an excuse to work together anyway.
(Which, in canon!Worm, he wasn't.)
The other part of all of this is that if Taylor tells her story she's going to tell
everyone who hears about it exactly what Coil's power is. She saw something that didn't happen through precognition. The minute it started to go south it
never happened. That means that Coil's power is precognition - he foresaw Taylor "pulping" his team and retroactively didn't send them in.
Does that matter? Well, sort of. It won't have an immediate effect on what the gangs do. It will have an effect long-term if they realize Coil tends to drop timelines that go poorly. That's going to change their "rules of engagement" when dealing with Coil. Things like
there is no overkill or
self-destruct devices are your friend will become mandatory.
Coil's men show up? Break out the rocket launcher. Blow up their van, kill every single one of them, make it as messy as possible and don't care about police investigation.. because Coil will see that possible future, realize he just lost an entire team, and promptly discard that attack.
Can Coil work around this? Sure. Two or three attacks on the same target and he'll have snipers ready to take out the guys with the rocket launchers.. but that's more time, more irritation, and overall slower progress for Coil.
Somehow I just don't see Coil being happy about that..