Firstly, there wasn't actually much of the book centred on the Enterprise itself. I think there was more of a word count for Trip's activities than Mayweather's, T'Pol's and the Enterprise's combined.
I think that's the way it should be. This is an epic story spanning the whole of known space at the time. It would be too narrow a focus if it were strictly about the NX-01 crew. It's not an Enterprise novel in the sense that it's about NX-01, period; it's an Enterprise novel in the sense that it follows many characters established over the course of the television series of that name -- Hernandez, Shran, Soval, T'Pau, Kuvak, Samuels, Gral, Thoris, Gannet Brooks, Valdore, etc. -- and explores the roles they played in this sweeping historical event.
With the Andorian and Tellarite ships pulling out because they're taking heavy losses, and the Vulcans already having pulled out, it's clear why it is referred to as the Earth-Romulan war, but why is United Earth so eager to form up the Federation after this if we know our "allies" can't be trusted to have our backs? I can only guess that they finally help us drive the Romulans back and all is forgiven.
This book only covers the first year of the war. There are five years left before the UFP is founded. And remember, just five years before this, the Vulcans, Andorians, and Tellarites were at each other's throats and none of them had any use for humans. So things can change a lot in that time.