Anyway, the point is that:
1) The Federation have literally warped the laws of time and space to revive the tribbles, and are now actively seeking to cultivate them.
2) Tribbles are a dangerous biological weapon against Klingons and their worlds, for at least two reasons (severe allergies that for all we know may be life-threatening in some Klingons, and also the tribble ability to rapidly devour ecosystems when introduced as an endangered species).
3) Going by some of the duty mission titles, the Klingons are at least prepared to consider using biological weapons against their enemies.
4) In turn, it is reasonable to fear that the Federation may think it wise to use tribbles as a weapon against the Klingons
5) As supporting evidence, Kirk did precisely that on at least two separate occasions in the 23rd century- once in TOS, once in TAS.
So there is precedent and cause to think that the Federation's decision to literally engage in time travel and retrieve and cultivate tribble specimens is intended in some way as a weapon against the Klingon Empire.
Given that this is true, taking care of the tribbles may be objectively less important than, say, killing Borg. But that doesn't mean a handful of ships can't be spared for the purpose, especially if they're only going to be on that mission for a short period of time. After all, it is unlikely that half a dozen ships will make the critical difference against the Borg when dozens or hundreds of ships are already deployed to fight them.
