So, Starfleet has a doomsday weapon against the Q. The Q represent an existential threat to Starfleet Command that cannot be properly accounted for in risk-loss scenarios being calculated in war games being run by their top military commanders. They, in turn, would push for the weaponization of omega particles as a weapon of last resort. "If the Q decide to suddenly appear, we'll detonate this bitch and put a stop to their shenanigans once and for all."
Yeah, I get Starfleet is too "nice" to consider something like that, but I call BS because military commanders and tacticians are far more aware of the costs in life and property than the soldiers beneath thme because they deal with existential crises all the time and must be prepared to act accordingly. While it's highly likely there are only a handful of them, it is undoubtedly true Starfleet would have some form of JCoS who are tasked with making the hard decisions in war. That, in turn, would definitely lead to seeking an equalizer against the Q, if for no other reason than to prevent shenanigans like what happened on the TNG.
Now, I'll wait for you to respond because I'm sure I'm operating on incomplete information. From what I know so far, this would be my logical conclusion. I appreciate you in patiently explaining it to me, though!