Although it's still problematical if the movie is claiming that the Romulan Neutral Zone is mere hours from Earth, even at maximum warp for the E-E.
Not really let's not forget that Earth and Romulus have to be close enough so that their probably really slow ships that max out at warp 5 on the old scale (which 24th century ships can go considerably faster that) could reach each other in a considerably decent amount of time to fight the battles in the war between them.
Define "a decent amount of time." In the age of sail, it could take weeks or months to get to a battlefield. That didn't stop people from having wars. It took Archer and NX-01 months to find the Xindi. And in the novels, engagements in the Earth-Romulan War were generally weeks or months apart. Even with the faster warp factors of the 24th century, it should still take days at least, not hours, to get from Earth to the Federation border.
One of the rules in the writers' bibles for both TOS and TNG was "Do not treat deep space as a local neighborhood." Roddenberry never wanted the show to lose sight of the immensity of space and the difficulty of crossing it. He never wanted ships to be able to hop from planet to planet as easily as commuting to work, because that trivialized space travel. Sadly, that's a rule that Roddenberry's successors frequently ignored.