Why make it something other than the Enterprise? I don't get that mindset. Continuity is always evolving. New ideas and concepts are introduced, often filling in blank spots. By introducing the XCV 330, TMP opened to door for other starships named Enterprise. In the 200 years between First Contact and TOS there could have been several ships named Enterprise. We know of two for sure.
I'm also of the opinion that the events of FC always happened. Picard and the E were always there and meant to be there. There was no alternate timeline.