ENT didn't change everything as it did not portray the Romulan War.
It's not like Romulus is around the corner, so Romulans and Humans couldn't make contact (resp. come so close to each other that the Romulans feel threatened) without warp drive. As the Federation is founded after the war, humans must have been out there for some years and met Tellarites and Andorians.
In short, ENT makes perfect sense if you don't focus just on a few Spock lines but on the entire picture which includes first contact with the other three founding members of the Federation, the slow development of trust between them and the Romulans attempets to undermine this trust.
Furthermore Spock's statement only makes sense if there was a temporary technological regress during the war (before and afterwards warp technology is used). If the war is bloody, if the Romulan threaten to conquer Earth you don't need warp vessels, simple impulse drive will suffice. And H-bombs are probably simpler to produce than antimatter bombs aka photon torpedoes.