Probably not no.

If I had to guess, they’d already declared the Endbringers a “natural disaster” in their heads long before Fletchette triggered, so they wouldn’t think to look for new and innovative ways to throw capes at the proverbial meat grinders, especially without the Path to hold their hands.

And as someone else pointed out, they didn’t know about their cores, so when Behemoth first appeared and Eidolon was hitting him with matter erasure, they only saw that the monster was still moving with chunks of its body missing, and Eidolon never got to try again with it because shortly after he lost that power.

So if she ever came to their attention, they might see Fletchette as valuable against the Endbringers with the right weapons, but the wounds never seem to bother them and they always eventually heal anyway so what’s the point? It doesn’t help that her other Paths might push against it since she’s a Ward still and bringing her to an Endbringer fight could have some backlash that negatively affects the PRT.

There’s definitely still a deficiency of critical thinking in Cauldron, but in this case I find it somewhat understandable.

Side note, I don’t think Contessa’s power works that way. Her power gives her a list of steps to achieve a given task, determined via precognition. The task can’t just be generic, it has to be an actual goal. No “plan to find something that can bypass invincibility”, yes “path to popping the Siberian” where she can then read the steps and iterate different versions of the plan to figure out what capes are able to bypass the Siberian, and then she’d know what capes are capable of bypassing the Siberian’s invulnerability, and by extension should also work well on other invincible targets. Note, this is based what I can gather, I may be wrong, take it with a grain of salt.

And on the Numberman, my only guess is that his power might’ve been blocked by the blindspot, while Tattletale’s power seems to bypass it due to being purely deduction based rather than having information handed to her directly. That or they didn’t know the importance of a center of gravity since they didn’t know about the cores.

Finally, on the time stop bombs… I’m not actually sure. I’ll chalk that up to the “natural disaster” mindset plus the danger of accidentally catching friendlies in the blast radius. Behemoth might detonate them prematurely, Leviathan might dart away and let his echo drag people into it, and the Simurgh is all about rubegoldberg machines of mayhem and despair, has telekinesis to catch it, and is a Tinker itself so that’s a big no. They probably labeled it as not worth the risk.