At this point if they don't ask us for a patrol ship in the frigate/light cruiser range to help maintain and protect our borders, any sensible person would be accusing them of being bought off by the Klingons somehow. We need a huge number of hulls to both stabilize our borders after the Klingons waltzed in almost uncontested, as well as to secure the colonies which are so unprotected that pirates were fighting over who got control over them instead of against us. This is before we had a third of our fleet obliterated with more coming Soon™, which will only exacerbate the issue and further embolden extant pirates and likely generate new ones sensing weaknesses.If Starfleet Command asks us for a patrol frigate, we'll design a patrol frigate. But if it asks us for something else, it's well beyond our pay grade to decide we really ought to give it a patrol frigate instead.
Frankly Starfleet was failing its obligations before the Klingons attacked terribly, and if it wants to fulfill them and maintain itself as a government that supports its members instead of a human first club that lords over other peers, it needs more ships. Not science ships (although if we can fit that in I am down) or an engineering ship (While having one that's faster would be great, other than speed the Archer is a one stop shop for Light industry on the move) or even a transport ship (which if we can fit in more, great, but it isn't essential in most cases and we do have Archers, Excaliburs and other who can do it if need be) we need something to keep those that would mean us harm off our lawn.
Science while essential, can't be performed if the Klingons bludgeon us over our heads when we try. Infrastructure that we cannot defend or at worst deny to the enemy is money in their pocket to do yet more harm to us. The Federation is a nation of scholar that has ostensibly surrounded itself with a ring of spears. Except now the spears are broken. Shattered, and the scholars are under threat. We need more spears lest the figurative beasts at our door slake their hunger out on us.
So, we are going to need to pull a Stingray if the prompt isn't for a patrol ship, because otherwise the Federation will get invaded again and we will have failed them in our laxity.