Whilst you're right that one of our ships has basically no chance of responding to an attack in progress on one of our merchant ships, this has also been true for basically most of naval history. Modern navies might be able to respond to Somali pirate attacks as they're happening now, but only because a large number of warships are permanently sitting off the Horn of Africa. But if you go back decades or centuries, forget about it. There would be no realistic prospect of attacking a German surface raider in either World War or a 17th century pirate ship whilst it was in the process of attacking a merchant ship, unless you had warships already present. However, this isn't really the role of using small warships for anti-piracy work?
The point of an anti-piracy ship is to hunt pirates, not to arrive on the scene of a pirate attack like Batman intervening to stop a mugging. A navy will look at the pattern of attacks in an area, and sets up patrols to try and find pirate ships, locate pirate bases, assign warships as convoy escorts (although this is not ideal), or even disguise warships as merchant ships. This is honestly a good reason to go for the half-saucer too, because it means our ships will be more able to chase down pirate vessels when they encounter them, whether at impulse or at warp.
To be clear, we could probably have done a version of this if we'd gone for armed cargo ships, although I expect that dedicated frigates with polarised hull plating will be more capable combatants. But the concept of anti-piracy patrols is not invalid, and I think it's worth keeping in mind as we go forward.