They wouldn't be as advanced as the top of the line NX Class
Why when facing war with a interstellar technological species like the Romulans, would Humans deliberately build a lessor advanced starship than they already had? The Daedalus would be state of the art in every way, and yes would be designed to be built in large numbers and quickly. Unlike the NX class being built laissez-faire, perhaps for budgetary reasons.
but if the war was mostly a defensive one, a fleet capable of warp 4 wouldn't be entirely useless. Plus, we don't really know what happened during the war
We know that the war was able to push the Romulans back to the edge of their own home star system.
That doesn't sound like defensive, it sounds like Earth went on the aggressive. Not some little skirmish, more a massive World War Two level of effort. And it was bad enough that a century later there were still Earth outposts monitoring "the border."
Hypothetical on my part, one way to reconcile is that Starfleet wasn't the only, or largest, of Earth's various and numerous fleets of defense/exploration starships. Resulting in the Earth/Romulan war being fought by a Earth Interstellar Defense force whose organization Starfleet was a minor part of.
The show Enterprise never made it clear what Starfleet's upper ultimate authority was. Was United Earth Space Probe Agency the entirety of Earth's nations, or only a few?
Q said in the first TNG episode that after the third world war it wasn't only United Earth, there was also a New United Nations.