The main issue is that this ship has exactly one job: Kill Klingon Battlecruisers. It's not a patrol ship, it's not a raider, it's certainly not an exploration vessel; it's a big knobbly stick with nails in to bash Klingons over the head with until they stop trying to conquer the Federation. That's it.
I don't disagree, merely point out that with higher cruise range it's more likely to be close enough to respond in time given it's patrolling a similar area to a slower craft while on the other hand with a faster sprint it's response radius and times within that radius from it's current location is effectively larger and faster.
Both can have similar effects but doctrine and usage will change depending on the choice. Regardless if it's to be effective it's going to have to patrol to some degree as Starfleet can't build and crew enough to cover every (relevent) cubic lightyear of it's space, not even just the border regions. Further patrols add uncertainty to hostile actor's ability to plan as static basing means predictable range and response times to incursions.
Now the Klingon's want a fight so it's not a problem with them but outside of that war their going to be scaring the crap out of would be pirates and the like that one could be nearby. Even with the Klingon's that their might be two of them in the same theater of operation is going to make them ask if it's worth poking the nest. That however runs back in a circle round to quantity, loiter time in the black, response time and radius and Klingon intelligence on Starfleet dispositions.